Probes and pressure modulation algorithms for reducing extratissue contamination in hemodynamic measurement

ABSTRACT

The present disclosure provides devices and methods for improved hemodynamic monitoring, including techniques for reducing signals related to hemodynamic activity outside the tissue or region of interest.

RELATED APPLICATIONS

The present application claims priority to and the benefit of U.S.Patent Application No. 61/943,907, “Probes And Pressure ModulationAlgorithms For Reducing Extratissue Contamination In HemodynamicMeasurement” (filed on Feb. 24, 2014); U.S. Patent Application No.62/091,048, “Probes And Pressure Modulation Algorithms For ReducingExtratissue Contamination In Hemodynamic Measurement” (filed on Dec. 12,2014); and U.S. Patent Application No. 62/091,064, “Pressure Modulation,Motion Detection, Individualized Geometry, And Improved Optic-SkinCoupling To Improve Long Term Clinical Monitoring With Diffuse Optics”(filed on Dec. 12, 2014). All of the foregoing applications areincorporated herein by reference in their entireties for any and allpurposes.

GOVERNMENT RIGHTS

This invention was made with government support under grant numbersR01-NS060653, NHLBI-HL007915, and 8P41-EB015893 awarded by the NationalInstitutes of Health. The government has certain rights in theinvention.

TECHNICAL FIELD

The present disclosure relates to the field of spectroscopic hemodynamicmonitoring.

BACKGROUND

As but one example of the importance of hemodynamic information,cerebral oxygen delivery is critical in maintaining cognitive functionand in the successful development of the young brain. Cerebral bloodflow is regulated to ensure sufficient oxygen delivery. However, thisblood flow autoregulation may be disrupted due to illness, injury, ormedical treatment; without longitudinal measurements of cerebral oxygendelivery practical for bedside measurements, clinicians must utilizeproxy measurements (e.g., systemic oxygenation) to anticipate andprevent ischemic brain injury. When the assumptions underlying theseproxy measurements fail, clinical interventions may be poorly chosen.

Diffuse Correlation Spectroscopy (DCS) and Diffuse Optical Spectroscopy(DOS; DOS may be considered equivalent to NIRS for purposes of thisdisclosure) devices have been used in the head and other organs tocontinuously measure blood flow, volume, and oxygenation at the bedside.Current clinical cerebral oxygenation monitoring techniques measureblood flow in large vessels (e.g., Doppler ultrasound), requiretransport to an imaging suite (e.g., MRI) or radioactive contrasts(e.g., PET), or are restricted to monitoring temporal trends (cerebraloximeters). Diffuse optics utilizes low power red light (non-ionizing),similar to that utilized in clinically ubiquitous pulse oximeters.

However, the clinical utility and inter-study comparisons of diffuseoptics are somewhat limited by technical challenges and instrumentvariability, restricting widespread adoption of diffuse opticaltechniques. Thus, there is a long-felt need in the art for improveddevices and methods for collecting and monitoring hemodynamicinformation in body tissues, including blood flow, volume, andoxygenation, as well as other data of interest.

SUMMARY

Provided herein are, inter alia, technical advances that reduceintermeasurement and subject variability while permitting longitudinalmeasurements. One advance provided herein is the control and modulationof pressure applied to a patient's anatomy by an optical probe,accomplished by utilizing the pressure-dependent portion of the diffuseoptical to separate signals from tissue (e.g., brain) and extra-tissue(e.g., extra-cerebral) signals. Non-invasive diffuse optics instrumentsmeasure optical signals that are influenced by hemodynamic contributionsfrom the tissue (brain, cerebral region) but also the region exterior tothat tissue (e.g., scalp and skull, extra-cerebral region). To improvetreatment management with DCS and/or DOS (e.g., for stroke), it isdesirable to accurately isolate and monitor hemodynamics (e.g., bloodflow changes) in real time, e.g., U.S. Pat. No. 8,082,015 (Yodh et al.),incorporated herein by reference in its entirety for any and allpurposes.

One may achieve real time monitoring with DCS (and/or with DOS) when thetissue in question (e.g., the head) is simplistically approximated as asemi-infinite homogeneous medium. This model, however, ignoresdifferences between blood flow outside of the tissue (e.g., in the scalpand skull in the case of monitoring blood flow within the head) andblood flow in the tissue of interest.

In the illustrative example of cerebral blood flow, blood flow in thescalp and skull especially can affect the DCS (and/or DOS) signal, whichin turn can lead experimenters to incorrectly assign physiologicalresponses to deeper brain tissue. Further, inconsistent pressure appliedon the head as the probe is being fastened can significantly alter theresults of a DCS blood flow measurement. The pressure applied on thescalp directly affects the blood flow in the extra-cerebral region. Whenused with simplified homogeneous brain models, these measurements cannotbe compared across patients and studies without an accurate measurementof the probe pressure. It should be understood, however, that theexample of cerebral blood flow is illustrative only, as the disclosedmethods and devices are not necessarily limited to use in cerebralstudies. For example, the disclosed technologies may be used to collect,monitor, and analyze hemodynamic information from various body tissues,including the brain, the breast, muscle, joints, tumors, internalorgans, and the like.

It should be understood that the disclosed methods and devices may beapplied to DCS, DOS (also NIRS), or any combination thereof. Where thisdisclosure mentions DCS measurement, it should also be understood thatthe disclosed technology may in some embodiments also perform DOSmeasurement with the DCS measurement (or even in place of the DCSmeasurement) should the user decide to do so. Likewise, where thisdisclosure mentions DOS measurement, it should also be understood thatthe disclosed technology may in some embodiments also perform DCSmeasurement with the DOS measurement (or even in place of the DOSmeasurement) should the user decide to do so. Put another way, DCS andDOS may be performed together, sequentially, or singly, and should beconsidered interchangable. It should further be understood that wherethe term “blood flow” is mentioned, the term is illustrative only and isintended to illustrate but one of several hemodynamic quantities thatmay be measured and/or evaluated. Thus, where the term “blood flow” ismentioned, the present disclosure also contemplates one or more of bloodflow, blood volume and saturation.

There is hence a clear need to monitor the probe pressure in astandardized manner and as well as develop methods to remove the effectsof blood flow from the extra cerebral components of the brain.

The present disclosure provides using pressure elements with opticalprobes, e.g., using an air bladder to control applied pressure as wellas an element to sense the applied pressure. Algorithms may be used toisolate blood flow contributions from the tissue of interest.

Turning again to the non-limiting example of cerebral blood flow, onemay use algorithms to isolate the cerebral blood flow contributions fromthe cortex from DCS (i.e., DCS and/or DOS) data using measurements atmultiple pressures and optical source-detector separations. Pressure onthe scalp may affect the blood flow in the extra-cerebral region.

For this reason, one may modulate pressure with an air bladder to permitcontinuous variation of the pressure applied to the skin, permittingcontinuous slow time scale (e.g., about 1-3 sec to about 10 min)modulation of the superficial blood flow. Such modulation imposes acarrier wave on the superficial signal, but not affect the cerebralsignal, and thus permit separation of cerebral blood flow. Again, thedisclosed techniques are not limited to cerebral applications or the useof any particular device to modulate pressure, as the foregoing exampleis illustrative only.

Regarding the illustrative application to cerebral blood flow, theoptical techniques of diffuse correlation spectroscopy (DCS) and diffuseoptical spectroscopy are a noninvasive bedside, continuous, safemonitors of hemodynamics, e.g., cerebral blood flow (CBF) that improvesindividual patient management of stroke treatment as well as other braindiseases. To improve stroke treatment management with DCS and/or DOS, itis desirable to accurately monitor hemodynamics (e.g., cerebral bloodflow changes) in real time. One may achieve real time monitoring withDCS/DOS by approximating the head as a semi-infinite homogeneous medium,i.e., the tissue is assumed to have spatially uniform blood flow overthe sampled volume. One drawback of this model, however, is that itignores differences between extracerebral blood flow (e.g., in the scalpand skull) and cerebral blood flow. Blood flow in the scalp and skullcan affect the DCS signal and can lead experimenters to incorrectlyassign physiological responses. Thus, a need for translation of DCS intothe stroke clinic is a method for quickly removing extracerebralcontamination in DCS cortical signals.

To handle heterogeneities in superficial (e.g., extra-cerebral) tissues,more complex, computationally intensive models have been proposed,including layered diffusion models and Monte Carlo techniques inrealistic geometries of the head and other parts of the anatomy. But thecomplexity of these models generally makes it impractical to implementthem for real time measurements of cerebral blood flow. Further, thesemodels often require a priori anatomical information about the patient,which information may not always be available.

In one aspect, the present disclosure provides algorithms to reduceextracerebral contamination in DCS/DOS measurements of the brain in realtime by acquiring DCS/DOS measurements of the head at multiple probepressures and source-detector separations. Variations in the probepressure against the head induce variations in extracerebral blood flowwhile cerebral blood flow remains constant, which permits the derivationof patient-specific analysis parameters to isolate cerebral blood flowsignals. As explained below, this technique does not require a priorianatomical information, and is not limited to cerebral applications.Further, pressure is but one perturbation that a use might use toisolate tissue (e.g., cerebral) blood from superficial (e.g.,extracerebral) blood flow and/or volume.

With specific regard to one non-limiting cerebral application to whichone may put the disclosed technology, to reduce extracerebralcontamination in cortical DCS/DOS measurements, an algorithm may use“initial” DCS/DOS measurements of the head at two (or more) differentprobe pressures against the scalp. One may demonstrate that increasedprobe pressure on the head induces decreases in scalp flow, but notcerebral flow. Hence, one way to remove extracerebral contamination isto apply a probe pressure high enough to reduce extracerebral blood flowto zero. Although this ensures that DCS/DOS does not measure blood flowin the scalp, probe pressure required to eliminate extracerebral bloodflow may in some cases be too high for long term clinical monitoring.The disclosed approaches also use probe pressure to remove extra-tissue(e.g., extra-cerebral) contamination. However, instead of relying on onesource-detector separation at a very high pressure, this approach usestwo separations at two different pressures that are both low enough tobe acceptable for clinical monitoring. It should be further understoodthat three, four, or more separations may be used at one, two, three,four, or more pressures.

The schematic in the left panel of exemplary, non-limiting FIG. 1 showsan illustrative instrument configuration that noninvasively probes thehead with short and long source-detector separations: ρ_(s)˜0.5 cm andρ_(l)˜2.5 cm. To distinguish extracerebral flow from cerebral flow, thehead may be modeled as a two-layer medium (scalp+skull and brain),although the anatomy is considerably more complex. Source-detectorseparations may be chosen such that detected light from the longseparation interrogates both layers, but detected light from the shortseparation is almost exclusively sensitive to the extracerebral layer.The specific source-detector separations are chosen based on subjectanatomy, e.g., a neonate has a thinner skull+scalp layer than adults andrequires appropriately scaled interfaces.

One may extend the Modified Beer Lambert Law to the DCS measurement.This formulation is particularly convenient in separating superficialand deep (e.g., skull/scalp and brain) DCS flow signals through aperturbation which changes blood flow in the superficial tissue, but notthe deep tissue. In the following non-limiting example, we describeapplication of external force to the tissue-optical interface to reduceblood flow in the scalp without effecting the brain. Formally, thisextension is derived by truncating the Taylor series expansion of thelogarithm of the electric field autocorrelation function at monitoringtime point t, delay time τ, source-detector separation ρ_(l), and probepressure P (i.e., log g₁(t,τ,ρ_(l),P)) to first order:

$\begin{matrix}{{{- {\log ( \frac{g_{1}( {t,\tau,\rho_{l},P} )}{g_{1,0}( {\tau,\rho_{l},P_{0}} )} )}} \approx {{{- {\frac{\partial}{\partial F_{ec}}\lbrack {\log \; {g_{1,0}( {\tau,\rho_{l},P} )}} \rbrack}}\Delta \; {F_{ec}( {t,P} )}} - {{\frac{\partial}{\partial F_{c}}\lbrack {\log \; {g_{1,0}( {\tau,\rho_{l},P} )}} \rbrack}\Delta \; {F_{c}(t)}}}} = {{{L_{ec}( {\tau,\rho_{l},P_{0}} )}\Delta \; {F_{ec}( {t,P} )}} + {{L_{c}( {\tau,\rho_{l},P_{0}} )}\Delta \; {F_{c}(t)}}}} & (1)\end{matrix}$

Here, g_(1,0)(τ,ρ_(l),P₀) is the “baseline” (i.e., t=0, P=P₀) measuredelectric field autocorrelation function when the extracerebral andcerebral DCS flow indices are F_(ec,0)(P₀) and F_(c,0), respectively.The multiplicative factors L_(ec)(τ,ρ_(l),P₀) and L_(c)(τ,ρ_(l),P₀) areDCS analogues to the partial differential pathlengths in the ModifiedBeer Lambert law. The temporal changes in extracerebral and cerebralflows from baseline are denoted by ΔF_(ec)(t,P)F_(ec)(t,P)−F_(ec,0)(P₀)and ΔF_(c)(t,P)≡F_(c)(t)−F_(c,0), respectively.

One may be interested in temporal cerebral blood flow changes(˜ΔF_(c)(t)), for example, prior to, during, and following clinicalinterventions. Because Equation 1 is linear, it can be solved quicklyfor real time display of these changes. However, in order to utilizeEquation 1 to extract ΔF_(c)(t) from the measured field autocorrelationfunction, one may require knowledge of L_(ec), L_(c), and ΔF_(ec). Asillustrated in the right panel of FIG. 1 and also in FIG. 3, thesemi-infinite model can be accurately applied to DCS measurements at theshort source-detector separation to extract ΔF_(ec) from g₁(t,τ,ρ_(s),P)and g_(1,0)(τ,ρ_(s),P₀).

As outlined in FIG. 1, a semi-infinite solution is fit to data collectedat the short source-detector separation to provide F_(ec,0), F_(ec,P),and these quantities are utilized as inputs to a two-layer model fitsimultaneously to two correlation curves acquired at different probepressures at the long source-detector separation for the extracerebrallayer thickness, d, and F_(c,0). The two layer correlation diffusionequation solution is used to evaluate the partial derivatives inEquation 1 to obtain L_(ec) and L_(c). It should again be understoodthat although the foregoing discussion is focused on cerebralapplications, the disclosed techniques may be generalized and applied toessentially any patient tissue. It should also be understood that atissue being studied may be modeled as having two, three, four, or evenmore layers. Likewise, it should be understood that measurements may bemade at one, two, three, or more pressures.

Another advance is integrated diffuse optic sensors. Traditionally, DCSand DOS measurements are carried out with rigid or semi-rigid probesusing a ‘one size fits most’ paradigm. But implementing this paradigm isdifficult because of the differences in anatomy (e.g., head) curvaturesbetween neonates and adults or even between locations on the adult head.Rigid flat probes are only useful in certain anatomies and locations.Semi-flexible probes, which can be forced to conform to the head orother parts of a patient's anatomy, are widely used, but are not stablefor long-term measurements and may cause pressure sores. In highlyunstable or delicate patients, the pressure required to deform the probemay be clinically unsafe. Furthermore, the flexibility of thesesemi-rigid probes is usually at the expense of changes in sourcedetector separation, which causes increased uncertainty of the measuredhemodynamic values. A change in source-detector separation of only about0.5 mm can result in changes in detected signal and calculatedphysiological properties. Flexible flat probes must be forced intoconformation with the head or other anatomy, potentially leaving airgaps between probe and skin, reducing measurement signal to noise ratio.

There is thus a need for probes that maintain contact with the skin andretain original source detector separations. One may address thischallenge with integrated paradigm for optical sensors that begins withanatomical imaging (e.g., head MRI, limb MRI), utilizes 3D printing toproduce a mold matching the curvature of a particular location on aspecific subject's anatomy (e.g., head), and produces a curved semirigid probe that conforms well to the subject. Furthermore, one mayinsert non-stretchable mesh into probes to permit flexibility withoutchanging the source-detector separations. An individually customizedprobe will enhance both data quality and patient comfort whilepermitting long-term serial monitoring over days or weeks.

Accordingly, in one aspect the present disclosure provides methods.These methods include measuring a motion of moving scattering particlesin a subject's cerebral region, the measuring comprising illuminatingthe cerebral region and collecting illumination with a firstsource-detector pair and with a second source-detector pair, the sourceand detector of the first pair being separated by (a) a first distanceand the source and detector of the second pair being separated by (b) asecond distance. The pressures applied to the subject's cerebral regionat or proximate to the locations of the first source and the secondsource are suitably different from one another, and one or both of thepressures is suitably applied to as to induce variations in superficialhemodynamics. One may isolate a deeper hemodynamic signal from thecollected illumination. By hemodynamics is meant a characteristic ofblood, e.g., flow, volume, pulsatility, oxygenation, viscosity, andother data of interest. The techniques described here also permitimproved measurement of concentration of other endogenous chromophores(e.g., cytochrome c oxidase, lipid, water); measurements of contrastagents, with fluorescence, absorption, bioluminescence, orphosphorescence; and serial measurements over days to months of therapy(e.g., monitoring chemotherapy efficacy).

Other methods provided herein include measuring a motion of movingscattering particles in a subject's tissue, the measuring comprisingilluminating the tissue and collecting illumination from a firstsource-detector pair and with a second source-detector pair, the sourceand detector of the first pair being separated by (a) a first distanceand the source and detector of the second pair being separated by (b) asecond distance, the pressures applied to the subject's tissue at orproximate to the locations of the first source and the second sourcebeing different from one another, one or both of the pressures beingapplied to as to induce variations in tissue hemodynamics, and isolatinga tissue hemodynamic signal from the collected illumination. Asexplained elsewhere herein, one may use source-detector pairs separatedby two, three, or more separation distances.

Also provided are devices, comprising: a first illuminationsource-detector pair, the source and detector being separated by a firstdistance (a); a second illumination source-detector pair, the source anddetector being separated by a second distance (b); and an elementconfigured to apply a pressure between the device and the subject'sbody. As described elsewhere herein, these devices may further includean accelerometer or other motion sensor element.

Also provided are methods. The methods comprise measuring movingparticles in a tissue, the measuring comprising illuminating a firsttissue region and illuminating a second tissue region superficial to thefirst tissue region; with a first source-detector pair and with a secondsource-detector pair, collecting illumination scattered by theparticles, the source and detector of the first source-detector pairbeing separated by a first distance, the source and detector of thesecond source-detector pair being separated by a second distance, thesecond distance being greater than the first distance, the collectingbeing performed under application of (a) one or more perturbationsdirected to the second tissue region, (b) one or more perturbationsproximate to the location of the first source-detector pair, proximateto the second source source-detector pair, or proximate to both thefirst and second source-detector pairs, or (c) any combination of (a)and (b), at least one perturbation effecting a hemodynamic change in thesecond tissue region, and estimating a blood flow of the first tissueregion from the collected illumination.

Further provided are systems, the systems suitably comprising a firstillumination source-detector pair having a source and detector separatedby a first distance (a); a second illumination source-detector pairhaving a source and detector separated by a second distance (b),distances (a) and (b) being different from one another; an elementconfigured to apply a pressure between the device and the subject'sbody; a processor configured to estimate a tissue's blood flow fromillumination collected by at least one of the source-detector pairs.

Other methods include estimating a cerebral blood flow, comprisingformulating a first estimate of extracerebral blood flow; perturbingextracerebral tissue; formulating a second estimate of extracerebralblood flow related to the perturbation of extracerebral tissue; andformulating a final estimate of cerebral blood flow related at least inpart to the first and second estimates of extracerebral blood flow.

Still other methods disclosed herein include methods of monitoring ablood flow, comprising illuminating a tissue and a region superficial tothe tissue; modulating one or more pressures applied to the regionsuperficial to the tissue; collecting a blood flow signal related toillumination reflected by the tissue and to illumination reflected bythe region superficial to the tissue; and removing from the signal atleast a portion of the illumination reflected by the region superficialto the tissue.

In a further aspect, the present disclosure provides methods. Themethods suitably comprise measuring moving particles in a tissue, themeasuring comprising illuminating a first tissue region and illuminatinga second tissue region superficial to the first tissue region; with afirst source-detector pair and with a second source-detector pair,collecting illumination scattered by the particles, the source anddetector of the first source-detector pair being separated by a firstdistance, the source and detector of the second source-detector pairbeing separated by a second distance, the second distance being greaterthan the first distance, the collecting being performed underapplication of (a) one or more perturbations directed to the secondtissue region, (b) one or more perturbations proximate to the locationof the first source-detector pair, proximate to the second sourcesource-detector pair, or proximate to both the first and secondsource-detector pairs, or (c) any combination of (a) and (b), at leastone perturbation effecting a hemodynamic change in the second tissueregion, and estimating a blood flow of the first tissue region from thecollected illumination, wherein the estimating comprises application ofthe DOS/NIRS Modified Beer-Lambert law

BRIEF DESCRIPTION OF THE DRAWINGS

The file of this patent or patent application contains at least onedrawing/photograph executed in color. Copies of this patent or patentapplication with color drawing(s)/photograph(s) will be provided by theOffice upon request and payment of the necessary fee. The summary, aswell as the following detailed description, is further understood whenread in conjunction with the appended drawings. For the purpose ofillustrating the invention, there are shown in the drawings exemplaryembodiments of the invention; however, the invention is not limited tothe specific methods, compositions, and devices disclosed. In addition,the drawings are not necessarily drawn to scale. In the drawings:

FIG. 1. Two exemplary source-detector pairs (with separations ρ_(l) andρ_(s)) sample tissue volumes as schematically indicated by so-called“banana patterns” of photon propagation (left). The head is modelled astwo-layer medium. The extracerebral top layer has a thickness d and DCSflow index F_(ec), while the cerebral bottom layer (brain) has a DCSflow index F_(c). Note that F_(ec) depends on the probe pressure Pagainst the scalp, but F_(c) does not. Simulated DCS data of the head attwo probe pressures (right) were generated from two-layer solutions ofthe correlation diffusion equation calculated with a top layer thicknessof d=0.9 cm and cerebral and extracerebral optical properties and bloodflow levels representative of the brain and scalp at these two probepressures. Noise was added to the simulated data using a correlationnoise model. The semi-infinite model was fit to the simulated data atthe short separation, ρ_(s), to accurately extract F_(ec) at both probepressures. These extracerebral flow indices were then used as inputs ina two layer model to simultaneously fit both correlation curves at thelong separation, ρ_(l), for d and F_(c). The solid lines in the rightpanel are these fits to the data, and the recovered fitted parameters,d=0.91 cm and F_(e)=1.12·10⁻⁸ cm²/s, agree well with the actualparameters, d=0.90 cm and F_(c)=1.10·10⁻⁸ cm²/s.

FIG. 2: Fractional cerebral blood flow changes calculated from the“probe pressure modulation algorithm” (i.e., Equation 1) and from thesemi-infinite model versus the actual cerebral blood flow changes insimulated DCS data of the head under conditions of constantextracerebral blood flow (left) and varying extracerebral blood flow(right). The baseline simulated DCS data (F_(c,0), F_(ec,0)) is depictedin the right panel of FIG. 1, and the simulated DCS data at differentcerebral and extracerebral flow levels was generated the same way asdescribed in connection with FIG. 1.

FIG. 3: (left) A portable DCS/DOS instrument with attached fiber optics,(middle) prism coupled exemplary DCS/DOS fiber optic probe with twosource-detector separations, and (right) schematic and photo ofexemplary fiber optic probe with 5 prisms and 2 pressure sensors,balloon for pressure modulation and elastic band. An embeddedaccelerometer is not shown.

FIG. 4: a 3-D rendering of an exemplary, non-limiting curved probe withaccelerometer.

FIG. 5: A flowchart of an exemplary algorithm to derive patient-specificlayer properties to be used to isolate CBF via Eq. 1 during clinicalmanipulation

FIG. 6: (left) Relative change in CBF during intravenous administrationof normal saline to a patient with a large left sided stroke. The timecourses have been averaged with a N=5 moving average window (right)Summary of average change in CBF in all patients due to intravenousadministration of normal saline. Contralateral hemisphere data are theleft bar at each patient #, and ipsilateral hemispherical data are theright bar at each patient #.

FIG. 7: A flowchart of an exemplary method—applying the DCS ModifiedBeer-Lambert law—for estimating a blood flow.

FIG. 8 (A) Schematic for blood flow monitoring in a homogeneous,semi-infinite turbid tissue. Blood cell motion (dark disks at time t,lighter disks at time t+τ) induces temporal fluctuations in thescattered light intensity, I(t), at the light detector (panel B). Theseintensity fluctuations are characterized by the normalized intensityauto-correlation function (g₂(τ)). (C) The decay of the intensityauto-correlation function curves is related to tissue blood flow.

FIG. 9 (A) The semi-infinite multiplicative weighting factors (see Eq.(4)) for tissue scattering (d_(s)), for tissue absorption (d_(a)), andfor tissue blood flow (d_(F), right y-axis). They are plotted as afunction of the correlation time, τ, for source-detector separation, ρ=3cm, and optical wavelength, λ=785 nm, given a typical set of cerebraltissue properties, i.e., μ_(a) ⁰=0.1 l/cm, λ_(s)ζ⁰=8 l/cm, F⁰=10⁻⁸cm²/s, n=1.4, n_(out)=1. (B) The semi-infinite DCS Modified Beer-Lambertcomponents d_(F)(τ,ρ)ΔF, d_(s)(τ,ρ)Δμ_(s), and |d_(a)(τ,ρ)Δμ_(a,c)|,plotted as a function of τ for a 10% increase in blood flow, tissuescattering, and tissue absorption, respectively. On the right y-axis isthe intensity auto-correlation function, g₂ ⁰(τ), for β=0.5. Given thesame fractional change, the DCS signal is most sensitive to scatteringchanges, followed by flow changes, and least sensitive to absorptionchanges.

FIG. 10: An exemplary two-layer tissue geometry;

FIG. 11: (A) The two-layer multiplicative weighting factors (see Eq.(9)) for d_(F,c) and d_(F,ec) (right y-axis); and for d_(a,c), d_(a,ec),d_(s,c), and d_(s,ec). They are plotted as a function of the correlationtime, τ, for source-detector separation, ρ=3 cm, and optical wavelength,λ=785 nm, given a set of typical extra-cerebral and cerebral tissueproperties, i.e., μ_(a,c) ⁰=0.16, μ_(a,ec) ⁰=0.12, μ_(s,c)′⁰=6,μ_(s,ec)ζ⁰=10 l/cm; F_(c) ⁰=10⁻⁸, F_(ec) ⁰=10⁻⁹ cm²/s; l=1 cm, n=1.4,and n_(out)=1. (B) The two-layer DCS Modified Beer-Lambert componentsd_(F,c)ΔF_(c), d_(F,ec)ΔF_(ec), |d_(a,c)Δμ_(a,c)|, and|d_(a,ec)Δμ_(a,ec)|, plotted as a function of τ for a 10% increase ineach parameter. On the right y-axis is the intensity auto-correlationfunction, g₂ ⁰(τ), for β=0.5. Notice that at shorter delay-times for ρ=3cm, the change in DCS optical density is about equally sensitive tochanges in cerebral blood flow, extra-cerebral blood flow, and cerebralabsorption. The change in DCS optical density is less sensitive tochanges in extra-cerebral absorption. (C) The ratio of the cerebral (c)and extra-cerebral (ec) flow components in the DCS optical densityperturbation, ΔOD_(DCS)(τ) (Eq. (9)), for 4 separations, ρ=0.5, 1, 2,and 3 cm. They are plotted as a function of τ for a 10% increase incerebral and extra-cerebral blood flow. For the shorter separations of0.5 and 1 cm, the ratio is substantially less than one, indicating thatthe DCS optical density is predominantly sensitive to the extra-cerebrallayer. At the 3 cm separation, the DCS optical density is slightly moresensitive to cerebral blood flow than extra-cerebral blood flow at theshort delay-times, i.e., the ratio is greater than one. However, atlonger delay-times, the ratio decreases, and the DCS optical densitybecomes more sensitive to extra-cerebral blood flow. (D) The ratio ofthe cerebral and extra-cerebral absorption components in the two-layerModified Beer-Lambert law for NIRS, plotted as a function of ρ for a 10%increase in cerebral and extra-cerebral absorption. (L) and (L)_(ec) arethe cerebral and extra-cerebral partial pathlengths. One may see frompanels (B) and (C) that the DCS optical density is more sensitive to thecerebral layer than the NIRS optical density is.

FIG. 12: (A) Simulated semi-infinite intensity auto-correlation curves(mean±SD across N=10k curves) plotted as a function of the delay-time τfor a −50% and 50% change in flow while tissue optical properties wereheld constant. The source-detector separation, light wavelength, andbaseline tissue properties are ρ=3 cm, λ=785 nm, and μ_(a) ⁰=0.1 l/cm,μ_(s)′⁰=8 l/cm, F⁰=10⁻⁸ cm²/s, n=1.4, n_(out)=1, respectively. Thesimulated DCS data were generated from applying a correlation noisemodel to the semi-infinite solution of the correlation diffusionequation (Eq. (5)). The correlation noise model was evaluated at abaseline DCS intensity of 50 k photons a second and an averaging time of2.5 seconds. (B) Fractional blood flow changes (mean±SD) estimated byapplying the semi-infinite DCS Modified Beer-Lambert law, i.e.,rbf(τ)=ΔOD_(DCS)(τ)/(d_(F)(τ)F⁰) (Eq. (4)), to the simulated data. Toappreciate the simulated results more generally, these fractional bloodflow changes are plotted against the dimensionless delay-time τγ⁰F⁰.(γ⁰F⁰)⁻¹, wherein γ≡K₀(μ_(s)′/μ_(a))(k₀)²r₁ (see Eq. (17)), isapproximately the characteristic decay time of the baseline electricfield auto-correlation function (see Appendix 2).

FIG. 13: Temporal fractional cerebral blood flow changes induced byinjection of the drug dinitrophenol (DNP) in a juvenile pig. Thebaseline flow is F⁰=5.34×10⁻⁸ cm²/s, which is the average blood flowindex over the 18 minute time interval between the vertical red lines.Cerebral blood flow changes were calculated from nonlinear fits to thesemi-infinite correlation diffusion solution (Eq. (5)) and from thesemi-infinite DCS Modified Beer-Lambert law (Eq. (4)) using (A) multipledelay-times, i.e., τ>5.5 μs, which corresponds to g₂ ⁰(τ)>1.25, and (B)a single delay-time, i.e., τ=3.8 μs, which corresponds to g₂ ⁰(τ)=1.3.Measured tissue absorption changes (FIG. 7B) were incorporated in boththe correlation diffusion fit and the DCS Modified Beer-Lambert law.Tissue scattering was assumed to remain constant at μ_(s)ζ=8 cm⁻¹.

FIG. 14: (A) Fractional cerebral blood flow changes (Mean±SD; averagedacross indicated time intervals in the legend) as a function of thedimensionless delay-time τγ⁰F⁰ (see FIG. 5 caption) in a juvenile pig.(B) The pig's cerebral absorption over time, which was calculated fromapplying the semi-infinite Modified Beer-Lambert law (Eq. (1)) to themeasured NIRS intensity changes from baseline. The cerebral blood flowchanges in panel (A) were obtained from applying the semi-infinite DCSModified Beer-Lambert law to the measured intensity auto-correlationcurves and the measured cerebral absorption changes. The horizontalsolid and dashed black lines in panel (A) indicate the fractional bloodflow changes (Mean±SD) obtained from fits to the non-linearsemi-infinite correlation diffusion solution.

FIG. 15: Fractional blood flow changes (i.e., F/F⁰−1) computed fromapplying the semi-infinite DCS Modified Beer-Lambert law (Eq. (4)) withassumed baseline optical properties of μ_(a) ⁰ (vertical axis) andμ_(s)′⁰ (horizontal axis) to semi-infinite simulated data with noise.The actual blood flow and absorption changes are (A) 50% and 15%, and(B) −50% and −15%, respectively. Tissue scattering was constant, and theactual baseline properties (including simulated noise parameters) areidentical to those in FIG. 5, e.g., μ_(a) ⁰=0.1, μ_(s)′⁰=8 cm⁻¹. TheModified Beer-Lambert law was used to calculate the absorption changefrom the simulated light intensity change, wherein the assumed baselineoptical properties were used to compute the differential pathlength. Thebaseline flow index, F⁰, was extracted from a nonlinear fit of thesimulated baseline auto-correlation data to the semi-infinitecorrelation diffusion solution given the assumed baseline opticalproperties. Errors in the assumed baseline optical properties only havesmall effects on the computed fractional flow change.

FIG. 16 provides an exemplary device according to the presentdisclosure. An optical fiber or fiber bundle and prism are opticallycoupled to an optical element (e.g., formed from additive manufacturingtechniques) and an optical-skin interface. Structural elements surroundthe junctions.

FIG. 17 provides an illustration of basic DCS measurement. Moving redblood cells (dark disks at time t, lighter disks at time t+τ) within thesampled “banana shaped” tissue volume induce intensity fluctuations. Thefaster the motion, the faster the fluctuations.

FIG. 18 provides an overview of intensity fluctuations characterized bythe autocorrelation function. Intensity fluctuations are characterizedby an intensity autocorrelation function, g₂. The decay of g₂ overdelay-time τ is related to tissue blood flow. Quantitatively, theelectric field (E) autocorrelation function, G₁, satisfies a correlationdiffusion equation. The solution to the correlation diffusion equationdepends on a blood flow index, F, that is directly proportional totissue blood flow. The correlation diffusion approach to flow monitoringis to fit the measured intensity autocorrelation function to theelectric field autocorrelation solution in order to extract the bloodflow index, F.

FIG. 19 illustrates the Modified Beer-Lambert Law for flow. In analogyto the NIRS Modified Beer-Lambert law, the Modified Beer-Lambert law forflow relates changes in a DCS optical density, OD_(DCS), at delay time τto the blood flow change, ΔF. The multiplicative weighting factor d_(F)is the DCS analogue of the differential pathlength, and is evaluatedthrough numerically solving the flow derivative of the baseline DCSoptical density. The Modified Beer-lambert law for flow is a system ofequations, i.e., one equation for each delay-time, that can be rapidlysolved for flow in a least squares sense.

FIG. 20 illustrates a validation of the DCS Modified Beer-Lambert Law.The DCS Modified Beer-Lambert law for flow was validated on a pig. Thepig was given the drug dinitrophenol (DNP), which induced a big increasein cerebral flow. This increase was then calculated with the standardcorrelation diffusion approach and with the DCS Modified Beer-Lambertlaw. There is good agreement between the two techniques. Since theModified Beer-Lambert law only needs one delay-time instead of manydelay-times, it is theoretically possible to measure blood flow with ahigher measurement speed using the DCS Modified Beer-Lambert lawapproach.

FIG. 21 illustrates a multi-layer model of the head. Cerebral tissue iscommonly modelled as homogeneous, but in reality it is layered. Thepresence of a superficial layer strongly influences the measured signal,g₂, Thus, flow changes in the superficial layer will induce signalchanges, which contaminate the measurement of cerebral blood flow.

FIG. 22 presents a 2-layered Modified Beer-Lambert law for flow. Atwo-layer Modified Beer-Lambert law for flow can be used to reduceextra-cerebral contamination in cerebral monitoring, which relates thechange in DCS signal to changes in cerebral flow (ΔF_(c)) and changes inextra-cerebral flow (ΔF_(ec)). The two-layer model consists of ahomogeneous cerebral layer below a homogeneous extra-cerebralsuperficial tissue layer of thickness l. The weighting factors d_(c) andd_(ec) are DCS analogues of the NIRS partial pathlengths, and they areevaluated from taking the appropriate derivative of the baseline DCSoptical density.

FIG. 23 presents a 2-layered, 2-separation distance ModifiedBeer-Lambert Law for flow. To constrain the two-layer model, twosource-detector separations probe the head. One separation is short, andconsequentially only samples the extra-cerebral layer. There is atwo-layer DCS Modified Beer-Lambert law for each separation. This systemof two equations is solved for the cerebral flow change.

FIG. 24 presents a 2-layered, 2-separation distance ModifiedBeer-Lambert Law for flow. To solve for the cerebral flow change,knowledge of the ratio of extra-cerebral weighting factors and knowledgeof the long-separation cerebral weighting factor are required. Probepressure modulation permits the measurement of these parameters.

FIG. 25 presents probe pressure modulation calibration of DCS. Changingthe probe pressure against the head induces changes in signal at boththe long and short separations. It is assumed that these signal changesarise entirely from extra-cerebral contamination, because changing theprobe pressure should not affect cerebral flow.

FIG. 26 illustrates correlation functions measured at 2 pressures and 2separation distances. Dividing the long and short separation DCSModified Beer-Lambert laws for the pressure-induced signal changeenables direct measurement of the ratio d_(ec)(τ,ρ_(l))/d_(ec)(τ,ρ_(s)).Thus, through acquiring long and short separation measurements at twopressures, this key parameter for calculating cerebral flow can bemeasured in a patient-specific manner.

FIG. 27 cerebral blood flow with probe pressure calibration. Tocalculate the remaining unknown, d_(c), the numerical derivative of thelogarithm of the two-layer correlation diffusion solution (G₁), needs tobe evaluated. Evaluation requires knowledge of the baseline cerebralflow and layer-thickness. These can be determined by fitting the twolong-separation signals acquired at two probe pressures to the two-layercorrelation diffusion model. Constraints in this fit are that thepressure-induced cerebral flow change is zero, and that thepressure-induced extra-cerebral flow change is determined from the shortseparation measurements via semi-infinite homogeneous techniques.

FIG. 28 illustrates DCS pressure calibration on an adult subject.Results of two-layer fit for cerebral flow and the layer thickness on anexemplar subject. A blood pressure cuff wrapped around the head was usedto adjust the pressure.

FIG. 29 illustrates cerebral blood flow changes versus pressure in anadult subject. The fractional cerebral blood flow change over multipleprobe pressures against the head, as computed with the two-layer DCSModified Beer-Lambert law and as computed with the semi-infinitehomogeneous model at the long and short separations. The shortseparation semi-infinite calculation is the extra-cerebral fractionalflow change from increasing probe pressures. As the probe pressureapproaches venous pressure, the extra-cerebral flow goes to zero. Thelong separation homogeneous calculation of cerebral flow issubstantially contaminated by this extra-cerebral change, as evidentfrom the large computed decrease in cerebral flow. However, thetwo-layer DCS Modified Beer-Lambert law calculation of cerebral flow isnot sensitive to probe pressure variation, as should be the case. Thus,the two-layer DCS Modified Beer-Lambert law successfully removed theextra-cerebral contamination from the long separation signal.

FIG. 30 presents measured CBF response to finger tapping in an adultsubject.

FIG. 31 is a flow chart of a probe pressure modulation algorithm forcerebral tissue absorption monitoring (Δμ_(a,c)) with DOS/NIRS. In thecalibration stage, baseline long and short separation intensitiesmeasured at probe pressure P⁰ (I⁰(ρ_(l)),I₀(ρ_(s))) and at probepressure P≠P⁰ (I^(P)(ρ_(l)), I^(P)(ρ_(s))) are used to calculateΔOD^(long,P) and ΔOD^(short,P), which are then used to estimateL_(ec)(ρ_(l))/L_(ec)(ρ_(s)) (“DOS Calibration term 1). “DOS Calibrationterm 2” is the numerical evaluation of L_(c)(ρ_(l)), which requiresknowledge of the baseline tissue optical properties and theextra-cerebral layer thickness (l). Ideally, these baseline tissueproperties are measured. In the monitoring stage, DOS Calibration terms1 and 2 are employed to convert subsequent measurements of differentiallong and short separation optical density changes, i.e., ΔOD^(long) andΔOD^(short), to differential cerebral absorption changes via. Note thatthe baseline used for the calibration stage and for the monitoring stageis the same.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

The present invention may be understood more readily by reference to thefollowing detailed description taken in connection with the accompanyingfigures and examples, which form a part of this disclosure. It is to beunderstood that this invention is not limited to the specific devices,methods, applications, conditions or parameters described and/or shownherein, and that the terminology used herein is for the purpose ofdescribing particular embodiments by way of example only and is notintended to be limiting of the claimed invention. Also, as used in thespecification including the appended claims, the singular forms “a,”“an,” and “the” include the plural, and reference to a particularnumerical value includes at least that particular value, unless thecontext clearly dictates otherwise. The term “plurality”, as usedherein, means more than one. When a range of values is expressed,another embodiment includes from the one particular value and/or to theother particular value. Similarly, when values are expressed asapproximations, by use of the antecedent “about,” it will be understoodthat the particular value forms another embodiment. All ranges areinclusive and combinable.

It is to be appreciated that certain features of the invention whichare, for clarity, described herein in the context of separateembodiments, may also be provided in combination in a single embodiment.Conversely, various features of the invention that are, for brevity,described in the context of a single embodiment, may also be providedseparately or in any subcombination. Further, reference to values statedin ranges include each and every value within that range.

Exemplary Methods

One application of the disclosed methods is developing and translatingthe optical techniques of diffuse correlation spectroscopy (DCS) and DOSfor continuous bedside monitoring, e.g., of cerebral blood flow (CBF) inpatients with brain disorders. This information provides clinicians withobjective evidence about treatment need and efficacy.

In the illustrative but non-limiting example of patients with acuteischemic stroke, treatments are designed to maximize CBF in the brainregion affected by the stroke in order to minimize stroke-relatedneurological damage. Doctors can prescribe many different interventionsdesigned to increase CBF (e.g., hypertensive therapy, intravenoushydration, rtPA infusion) in stroke patients. However, each of theseinterventions has negative side effects and may not be effective (i.e.,increase CBF in the ischemic stroke lesion) for an individual patient.

Continuous real-time monitoring of CBF over the ischemic stroke lesionpermits the rapid assessment of the efficacy of a particular treatmentintervention. If doctors observe that a prescribed treatment is notincreasing CBF, then they can quickly test the CBF response toalternative treatments. In this way, CBF monitoring will substantiallyhelp clinicians optimize ischemic stroke treatment for each individualpatient.

Due to the lack of tools available for noninvasive bedside monitoring ofCBF, doctors currently must make decisions about treatment interventionsempirically, based on expectations of neurological deficits, or inresponse to clinical deterioration. But changes in patient symptomsassociated with the development of neurological deficits occur on aslower time scale than changes in CBF from a prescribed treatmentintervention.

By the time patients are on an ineffective treatment paradigm exhibitdeteriorating neurological symptoms, it may be too late to successfullyadminister alternative treatment. Thus, the detection of CBF changesbefore patients exhibit new symptoms is clinically valuable, because itis in this time window that the situation is most treatable.

The optical technique of diffuse correlation spectroscopy is useful as anoninvasive bedside, continuous, safe monitor of CBF that improvesindividual patient management of stroke treatment as well as other braindiseases. To improve stroke treatment management with DCS, it is highlydesirable for DCS/DOS to accurately monitor cerebral blood flow changesin real time.

Additionally, one may utilize diffuse optical spectroscopy (DOS) tomeasure tissue absorption and scattering and thence derive theconcentration of physiologically important chromophores (e.g., oxy- anddeoxy-hemoglobin). Together, DOS and DCS permit calculation of tissueoxygen metabolism.

One may achieve real time monitoring with DOS or DCS by approximatingthe head as a semi-infinite homogeneous medium, i.e., the tissue isassumed to have spatially uniform blood flow/volume/saturation over thesampled volume. One drawback of this model, however, is that it ignoresdifferences between extracerebral blood flow (e.g., in the scalp andskull) and cerebral hemodynamics. Blood flow in the scalp and skull canaffect the DCS signal and can lead experimenters to incorrectly assignphysiological responses in cerebral blood flow (CBF). It should beunderstood that one may extend these techniques to other parts of theanatomy besides the head, e.g., the breast, internal organs, and thelike, especially where a relatively pliable layer overlays a stifflayer.

To handle extracerebral heterogeneities, more complex, computationallyintensive models have been proposed, including layered diffusion modelsand Monte Carlo techniques in realistic geometries of the head. But thecomplexity of these models generally makes it impractical to implementthem for real time measurements of cerebral hemodynamics. Further, thesemodels may require a priori anatomical information about the patient'shead which may not always be available. Thus, one need for translationof DOS and DCS into the stroke clinic is a method for removingextracerebral contamination in optical measurements, both to permitreal-time flow monitoring and to improve the fidelity of the corticalsignals.

Provided is a novel algorithm to remove extra-tissue (e.g.,extracerebral) contamination in DCS/DOS measurements in real time byacquiring DCS/DOS measurements (e.g., of the head) at multiple probepressures and source-detector separations. Variations in the probepressure against the head induce variations in extra-tissue (e.g.,extracerebral) blood flow while tissue (e.g., cerebral) blood flowremains constant, which permits the derivation of patient-specificanalysis parameters to isolate tissue (e.g., cerebral) blood flowsignals. As explained in detail in the next section, this technique doesnot require a priori anatomical information.

Provided herein are exemplary measurement/analysis technique that shouldsubstantially improve data collection and interpretation. In someembodiments, the technology removes extratissue contamination in DCS orDOS measurements by employing DOS or DCS data collected from twosource-detector separations at two low probe pressures. The disclosedapproach uses two separations at two different pressures that are bothlow enough to be acceptable for clinical monitoring.

The schematic in FIG. 1 shows an instrument configuration thatnoninvasively probes the head with short and long source-detectorseparations: ˜0.5 cm and ˜2.5 cm. To distinguish extra-cerebral flowfrom cerebral hemodynamics, the head is modeled as a two-layer medium.

Source-detector separations may be chosen such that detected light fromthe long separation interrogates both layers, but detected light fromthe shorter separation is almost exclusively sensitive to theextracerebral layer.

As explained elsewhere herein, to relate temporal changes inextracerebral flow and cerebral flow to the temporal changes in themeasured DCS signal at the long separation, one may extend the so calledpartial pathlength version of the Modified Beer Lambert Law to DCSmeasurements. This procedure takes into account the contamination of theunderlying cerebral signal by the superficial scalp blood flow, but canbe applied to other parts of a patient's anatomy and is not limited tothe head or cerebral applications.

DOS or DCS measurements at the short source-detector separation (p_(s))reveal ΔF_(ec)(t), and since the short separation only samples thescalp, it is reasonable to apply the semi-infinite model to accuratelyextract superficial hemodynamics. Together, the measurements permitdeconvolution of the clinically important cerebral blood flow from theless important and highly variable scalp dynamics.

Provided below is an illustrative step-by-step procedure for DCSmonitoring of changes in cerebral blood flow due to treatmentinterventions. This procedure may be extended to other parts of the bodybesides the head and to models incorporating additional layers:

Patient-specific DCS measurement of extra-cerebral blood flow:

-   -   1. Acquire g₁(t_(P),τ,ρ_(l),P), g₁(t_(P),τ,ρ_(s),P),        g_(1,0)(ρ,ρ_(l),P₀) and g_(1,0)(ρ,ρ_(s),P₀), the steady state        field autocorrelation function measurements of the patient's        head for the long (ρ_(l)) and (ρ_(s)) source-detector        separations at the baseline probe pressure P₀ and a different        probe pressure P (exerted at time t_(p)).    -   2. Determine the pressure induced extracerebral flow change        (i.e. ΔF_(ec,P)≡F_(ec)(t_(P),P)−F_(ec,0)(P₀)) by using the        semi-infinite DCS approximation to extract the extracerebral        flow indices F_(ec,0)(P₀) and F_(ec)(t_(P),P) from the short        source-detector separation field autocorrelation functions        g_(1,0)(τ,ρ_(s),P₀) and g₁(t_(P),τ,ρ_(s),P) respectively.    -   3. Via Equation 1, calculate

${L_{ec}( {\tau,\rho_{l},P_{0}} )} = {{- \frac{1}{\Delta \; F_{{ec},P}}}{\log( {{g_{1}( {t_{p},\tau,\rho_{l},P} )}/{{g_{1,0}( {\tau,\rho_{l},P_{0}} )}.}} }}$

-   -   4. Simultaneously fit g_(1,0)(τ,ρ_(l),P₀) and        g₁(t_(P),τ,ρ_(l),P) to the full two layer DCS diffusion model        (Gagnon et al., Opt. Expr., 2008) in order to extract the        baseline cerebral flow index (F_(b,0)) and the extracerebral        layer thickness (L). Inputs in this fit will be F_(ec)(t_(P),P)        and F_(ec,0)(P₀) determined from step 2. Often, the thickness L        is already known for the patient (e.g., from an MRI scan), which        constrains this fit further.

5. Evaluate

${L_{b}( {\tau,\rho_{l},P_{0}} )} \equiv {- {\frac{\partial}{\partial P_{b}}\lbrack {\log \; {g_{1,0}( {\tau,\rho_{l},P_{0}} )}} \rbrack}}$

from the two layer DCS diffusion model's analytical expression forg_(1,0). Required inputs in this evaluation are F_(ec,0)(P₀), F_(b,0),and l.

Real time cerebral blood flow monitoring with DCS:

-   -   6. Administer desired treatment interventions to patient and        continually measure the field autocorrelation functions        g₁(t,τ,ρ_(l),P) and g₁(t,τ,ρ_(s)P).    -   7. As in step 2, extract the extracerebral flow index        F_(ec)(t,P) from the short separation autocorrelation function        g₁(t,τ,ρ_(s),P).    -   8. Given the inputs F_(b,0) (step 4), L_(b)(τ,ρ_(l),P₀) (step        5), L_(ec)(τ,ρ_(l),P₀) (step 3), g_(1,0)(τ,ρ_(l),P₀) (step 1),        g₁(t,τ,ρ_(l), P) (step 6), and        ΔF_(ec)(t,P)≡F_(ec)(t,P)−F_(ec,0)(P₀) (steps 7 and 2), solve        Equation 1 for the fractional cerebral blood flow change from        baseline:

$\begin{matrix}{{{{rCBF}(t)} \equiv \frac{\Delta \; {F_{b}(t)}}{F_{b,0}}} = {{- \frac{1}{F_{b,0}{L_{b}( {\tau,\rho_{l},P_{0}} )}}}{( {{\log ( \frac{g_{1}( {t,\tau,\rho_{l},P} )}{g_{1,0}( {\tau,\rho_{l},P_{0}} )} )} + {{L_{ec}( {\tau,{\rho_{l}P_{0}}} )}\Delta \; {F_{ec}( {t,P} )}}} ).}}} & (2)\end{matrix}$

Equation 2 assumes that changes in the electric field autocorrelationfunction, g₁(ρ,ρ_(l)) are dominantly due to blood flow changes, and thatthese blood flow changes are also small enough for the first orderTaylor series expansion in Equation 1 to be a reasonable approximation.Simulations how that Equation 1 accurately calculates cerebral flowchanges (i.e., within 5% of actual) for the actual range of changesbetween −50% and 100%.

The fit in step 7 above may be further constrained by acquiringcorrelation curves at multiple probe pressures, and incrementallymodifying the superficial blood flow; different pressures may each givea different autocorrelation function with the same baseline cerebralflow index. As discussed below, mechanical control of the probe pressurepermits continuous variation of the pressure-dependent signal,effectively superimposing a carrier wave on the superficial signal.

One may measure absorption changes with diffuse optical spectroscopy(DOS). The Modified Beer Lambert law for the photon fluence rate is theDOS analogue of Equation 1. Thus, an analogous procedure to steps 1-8above can be applied to extract extracerebral and cerebral absorptionchanges from DOS fluence rate measurements. It is straightforward toincorporate diffuse optical spectroscopy measurements of absorptionchanges into Equation 2 by including two additional terms in the Taylorseries expansion in Equation 1: L_(μ) _(a)_(,ec)(τ,ρ_(l),P₀)Δμ_(a,ec)(t,P) and L_(μ) _(a)_(,b)(τ,ρ_(l),P₀)Δμ_(a,b)(t). Here, Δμ_(a,ec) and Δμ_(a,b) are changesin extracerebral and cerebral absorption, respectively, and

$L_{\mu_{a}{ec}} \equiv {{- {\frac{\partial}{\partial\mu_{a,{ec}}}\lbrack {\log \; {g_{1,0}( {\tau,\rho_{l},P_{0}} )}} \rbrack}}\mspace{14mu} {and}}$$L_{\mu_{a}b} \equiv {- {\frac{\partial}{\partial\mu_{a,{ec}}}\lbrack {\log \; {g_{1,0}( {\tau,\rho_{l},P_{0}} )}} \rbrack}}$

are DCS partial absorption path lengths that can be evaluatedanalytically in the same way as described in step 5 above. Thecorrection to Equation 2 accounting for absorption changes is

$\begin{matrix}{{{rCBF}(t)} = {{- \frac{1}{F_{b,0}{L_{b}( {\tau,\rho_{l},P_{0}} )}}}{( {{\log ( \frac{g_{1}( {t,\tau,\rho_{l},P} )}{g_{1,0}( {\tau,\rho_{l},P_{0}} )} )} + {{L_{ec}( {\tau,\rho_{l},P_{0}} )}\Delta \; {F_{ec}( {t,P} )}} + {{L_{\mu_{a},b}( {\tau,\rho_{l},P_{0}} )}{{\Delta\mu}_{a,b}(t)}} + {{L_{\mu_{a},{ec}}( {\tau,\rho_{l},P_{0}} )}{{\Delta\mu}_{a,{ec}}( {t,P} )}}} ).}}} & (3)\end{matrix}$

An alternative formulation of the DCS Modified Beer-Lambert law forblood flow uses the intensity autocorrelation function, i.e., g₂(τ,ρ)≡

I(t,ρ)I(t+τ,ρ)

/

I(t,ρ)

²), where I(t,ρ) is the detected light intensity at time t andsource-detector separation ρ. Assuming constant tissue opticalproperties, the two-layer DCS Modified Beer-lambert law relates changesin a DCS optical density, ΔOD_(DCS), to changes in cerebral flow andextra-cerebral flow:

${{\Delta \; {OD}_{DCS}} \equiv {- {\log \lbrack \frac{{g_{2}( {\tau,\rho} )} - 1}{{g_{2}^{0}( {\tau,\rho} )} - 1} \rbrack}}} = {{{d_{c}( {\tau,\rho} )}\Delta \; F_{c}} + {{d_{ec}( {\tau,\rho} )}\Delta \; {F_{ec}.}}}$

Here, g₂(τ,ρ) is the measured autocorrelation function with cerebral andextra-cerebral flow indices of F_(c) and F_(ec), respectively, and g₂⁰(τ,ρ) is the “baseline” measured autocorrelation function with cerebraland extra-cerebral flow indices of F_(c) ⁰ and F_(ec) ⁰. Thedifferential changes in cerebral and extra-cerebral flow from baselineare ΔF_(c)≡F_(c)−F_(c) ⁰ and ΔF≡F_(ec)−F_(ec) ⁰, and d_(c)(τ,ρ)≡−∂log(g₂ ⁰(τ,ρ)−1)/∂F_(c) and d_(ec)(τ,ρ)≡−∂ log(g₂ ⁰(τ,ρ)−1)/∂F_(ec) areweighting factors that indicate the contributions of cerebral andextra-cerebral flow changes to the DCS signal change.

As described above, cerebral flow monitoring (i.e., ΔF_(c)) can beachieved with two source-detector separations: a long separation (ρ_(l))that samples both cerebral and extra-cerebral tissues, and a shortseparation (ρ_(s)) that predominantly samples extra-cerebral tissue(i.e., d_(c)(τ,ρ_(s))=0). The two-layer DCS Modified Beer-Lambert lawsfor the long and short separations are:

${{{\Delta \; {OD}_{DCS}^{long}} \equiv {- {\log \lbrack \frac{{g_{2}( {\tau,\rho_{l}} )} - 1}{{g_{2}^{0}( {\tau,\rho_{l}} )} - 1} \rbrack}}} = {{{d_{c}( {\tau,\rho_{l}} )}\Delta \; F_{c}} + {{d_{ec}( {\tau,\rho_{l}} )}\Delta \; F_{ec}}}},{{{\Delta \; {OD}_{DCS}^{short}} \equiv {- {\log \lbrack \frac{{g_{2}( {\tau,\rho_{s}} )} - 1}{{g_{2}^{0}( {\tau,\rho_{s}} )} - 1} \rbrack}}} = {{{d_{c}( {\tau,\rho_{s}} )}\Delta \; F_{c}} + {{d_{ec}( {\tau,\rho_{s}} )}\Delta \; {F_{ec}.}}}}$

Solving this system of equations for ΔF_(c), we obtain

${\Delta \; F_{c}} = {{\frac{1}{d_{c}( {\tau,\rho_{l}} )}\lbrack {{\Delta \; {OD}_{DCS}^{long}} - {\frac{d_{ec}( {\tau,\rho_{l}} )}{d_{ec}( {\tau,\rho_{s}} )}\Delta \; {OD}_{DCS}^{short}}} \rbrack}.}$

Evaluating the above equation for ΔF_(c) requires knowledge ofd_(c)(τ,ρ_(l)) and the ratio d_(ec)(τ,ρ_(l))/d_(ec)(τ,ρ_(s)). Collectingmeasurements at multiple probe pressures against the head enables thesetwo parameters to be measured.

An exemplary schematic of the disclosed methods is provided in FIG. 7.As shown in that non-limiting figure, the probe pressure modulationalgorithm for filtering superficial tissue contamination in cerebralblood flow monitoring may include a calibration stage and a monitoringstage. For the calibration stage, intensity autocorrelation functionmeasurements at a short separation (g₂ ^(P)(τ,ρ_(s))) and a longseparation (g₂ ^(P)(τ,ρ_(l))) are acquired at probe pressure P againstthe head. Then, the probe pressure is adjusted to a baseline value thatis different than P, and baseline short-separation and long-separationintensity autocorrelation function measurements are made, i.e., g₂⁰(τ,ρ_(s)) and g₂ ⁰(τ,ρ_(l)). The measurements g₂ ^(P)(τ,ρ_(l)) and g₂⁰(τ,ρ_(l)) are used to calculate the pressure-induced change in thelong-separation DCS optical density, i.e., ΔOD_(DCS) ^(long)|_(ΔP)≡−log[(g₂ ^(P)(τ,ρ_(l))−1)/(g₂ ⁰(τ,ρ_(l))−1)]. Similarly, the measurements g₂^(P)(τ,ρ_(s)) and g₂ ⁰(τ,ρ_(s)) are used to calculate thepressure-induced change in the short-separation DCS optical density,i.e., ΔOD_(DCS) ^(short)|_(ΔP)≡−log [(g₂ ^(P)(ρ_(s))−1)/(g₂⁰(τ,ρ_(s))−1)]. Calibration term 1, which is the ratio of thelong-separation extra-cerebral weighting factor to the short-separationextra-cerebral weighting factor, i.e., d_(ec)(τ,ρ_(l))/d_(ec)(τ,ρ_(s)),is equal to the ratio of ΔOD_(DCS) ^(long)|_(ΔP) to ΔOD_(DCS)^(short)|_(ΔP′). To see how, note that because ΔF_(ec)=0, the two-layerDCS Modified Beer-Lambert laws for a probe pressure-induced signalchange are ΔOD_(DCS) ^(long)|_(ΔP)=d_(ec)(τ,ρ_(l))ΔF_(ec) ^(P) andΔOD_(DCS) ^(short)|_(ΔP)=d_(ec)(τ,ρ_(s))ΔF_(ec) ^(P), where ΔF_(ec) ^(P)is the pressure-induced change in extra-cerebral flow. Dividing thesetwo equations results in d_(ec)(τ,ρ_(l))/d_(ec)(τ,ρ_(s))=ΔOD_(DCS)^(long)|_(ΔP)/ΔOD_(DCS) ^(short)|_(ΔP).

Further, the pressure-induced change in extra-cerebral flow (ΔF_(ec)^(P)) is determined from ΔOD_(DCS) ^(short)|_(ΔP) via the semi-infinitehomogeneous DCS Modified Beer-Lambert law (see W. B. Baker, A. B.Parthasarathy, D. R. Busch, R. C. Mesquita, J. H. Greenberg, and A.Yodh, “Modified Beer-Lambert law for blood flow,” Biomed. Opt. Express5, 4053-4075 (2014)). Finally, the measurements g₂ ^(P)(τ,ρ_(l)) and g₂⁰(τ,ρ_(l)) are simultaneously fit to a two-layer correlation diffusionmodel of light transport (G₁(τ,ρ_(l))) (see Baker et al.; see also D. A.Boas and A. G. Yodh, “Spatially varying dynamical properties of turbidmedia probed with diffusing temporal light correlation,” J. Opt. Soc.Am. A 14, 192-215 (1997)) for the baseline cerebral flow, F_(c) ⁰,baseline extra-cerebral flow, F_(ec) ⁰, and the extra-cerebral layerthickness, l. This fit is tractable because the pressure-inducedcerebral and extra-cerebral flow changes, i.e., ΔF_(c) ^(P) and ΔF_(ec)^(P), are known. As described above, ΔF_(ec) ^(P) is determined by theshort separation measurements, and it is assumed that probe pressurevariation does not affect cerebral flow, i.e., ΔF_(c) ^(P)=0. Thisknowledge constrains the fit by reducing the number of unknownparameters to fit for in the model from five parameters (F_(c) ⁰, F_(ec)⁰, F_(c) ^(P), F_(ec) ^(P), l) to three parameters (F_(c) ⁰, F_(ec) ⁰,l), which consequentially makes the fit more robust to noise. Withknowledge of F_(c) ⁰, F_(ec) ⁰, and l, the derivative of the logarithmof the two-layer correlation diffusion solution with respect to cerebralflow is evaluated to obtain the long-separation cerebral weightingfactor, d_(c)(τ,ρ_(l))=−2∂ log G₁(τ,ρ_(l))/∂F_(c), which is calibrationterm 2.

In the monitoring stage, cerebral blood flow changes from baseline,i.e., ΔF_(c)≡F_(c)−F_(c) ⁰, are determined. Here, g₂ (τ,ρ_(l)) andg₂(τ,ρ_(s)) are the measured long-separation and short-separationintensity autocorrelation functions at a perturbed tissue state frombaseline wherein the cerebral and extra-cerebral flows are F_(c) andF_(ec), respectively. With these measurements and the baselinemeasurements from the calibration stage, ΔOD_(DCS) ^(long)≡−log[(g₂(τ,ρ_(l))−1)/(g₂ ⁰(τ,ρ_(l))−1)] and ΔOD_(DCS) ^(short)≡−log[(g₂(τ,ρ_(s))−1)/(g₂ ⁰(τ,ρ_(s))−1)] are calculated and then combinedwith calibration terms 1 and 2 to compute

${\Delta \; F_{c}} = {{\frac{1}{d_{c}( {\tau,\rho_{l}} )}\lbrack {{\Delta \; {OD}_{DCS}^{long}} - {\frac{d_{ec}( {\tau,\rho_{l}} )}{d_{ec}( {\tau,\rho_{s}} )}\Delta \; {OD}_{DCS}^{short}}} \rbrack}.}$

A directly analogous method can be applied for cerebral opticalabsorption monitoring (i.e., Δμ_(a,c)) with light intensity measurements(I(ρ)). For cerebral absorption monitoring, ΔOD_(DCS) ^(long) andΔOD_(DCS) ^(short) above are replaced with ΔOD^(long)≡−log[I(ρ_(l))/I⁰(ρ_(l))] and ΔOD^(short)≡−log [I(ρ_(s))/I⁰(ρ_(s))],respectively. The weighting factor parameters d_(c)(τ,ρ_(l)) andd_(ec)(τ,ρ_(l))/d_(ec)(τ,ρ_(s)) are replaced with the partialpathlengths L_(c)(ρ_(l)) and L_(ec)(ρ_(l))/L_(ec)(ρ_(s)) (see F. Fabbri,A. Sassaroli, M. E. Henry, and S. Fantini, “Optical measurements ofabsorption changes in two-layered diffusive media,” Phys. Med. Biol. 49,1183-1201 (2004)). The ratioL_(ec)(ρ_(l))/L_(ec)(ρ_(s))=ΔOD^(long)|_(ΔP)|ΔOD^(short)|_(ΔP), and thepartial pathlength L_(c)(ρ_(l)), is determined from evaluating thederivative of the analytical two-layer photon diffusion Green's functionG(ρ_(l)) (using knowledge of the extra-cerebral layer thickness, l, andbaseline tissue properties), i.e., L_(c)(ρ_(l))=−∂log(G(ρ_(l)))/∂μ_(a,c). Cerebral absorption monitoring at multiple lightwavelengths in turn enables the computation of cerebral oxy-hemoglobin,deoxy-hemoglobin, and blood oxygen saturation (see T. Durduran, R. Choe,W. B. Baker, and A. G. Yodh, “Diffuse optics for tissue monitoring andtomography,” Reports on Progress in Physics 73, 076701 (2010)). This hasimplications for the growing field of functional near-infraredspectroscopy (fNIRS).

Results—Methods

The provided “probe pressure modulation” scheme was tested on simulatedDCS data of the head (FIGS. 1, 2). Baseline simulated DCS data of thehead was generated from adding simulated field autocorrelation functionnoise to two-layer solutions of the correlation diffusion equation atextracerebral and cerebral optical properties and flow levelsrepresentative of the scalp and brain. The cerebral blood flow was thenvaried from baseline while the extracerebral blood flow remainedconstant, which mimics localized cerebral blood flow responses tofunctional tasks such as finger tapping (FIG. 2, left panel).

In a second simulation data set, the cerebral blood flow was varied fromthe same baseline level while extracerebral blood flow also changed(FIG. 2, right panel), which is the case for more global flowperturbations such as hypercapnia that effect both the scalp and thebrain.

The probe pressure modulation scheme (Equation 1) and the semi-infinitemodel were both applied to these simulated data sets to calculate thecerebral blood flow changes, and the results are in FIG. 2. Theagreement between the calculated and actual cerebral blood flow changesis better when using the probe pressure modulation scheme than whenusing the semi-infinite model. The semi-infinite model is highlysensitive to the extracerebral layer. Thus, if the extracerebral flow isconstant, then the semi-infinite model underestimates the true cerebralblood flow changes. Similarly, changes in extracerebral blood flowaffect the calculated flow changes with the semi-infinite model.

Summary—Methods

The probe pressure modulation scheme described above on simulated DCSdata of the head has been successfully employed to calculate cerebralblood flow changes with substantially less extracerebral contaminationthan the semi-infinite model (FIG. 2). As with the semi-infinite model,this probe pressure modulation scheme can recover cerebral blood flowchanges in real time, and a priori anatomical information is notrequired. Of course, these techniques may be applied to other parts of apatient's anatomy.

In one aspect, the present disclosure provides methods. These methodsinclude measuring a motion of moving scattering particles (e.g., bloodcomponents) in a subject's cerebral region, the measuring comprisingilluminating the cerebral region and collecting illumination with afirst source-detector pair and with a second source-detector pair, thesource and detector of the first pair being separated by (a) a firstdistance and the source and detector of the second pair being separatedby (b) a second distance, the pressures applied to the subject'scerebral region at or proximate to the locations of the first source andthe second source being different from one another, one or both of thepressures being applied to as to induce variations in extracerebralhemodynamics, and isolating a cerebral hemodynamic signal from thecollected illumination. Such a signal may relate to, e.g., blood flow,volume, oxygenation, and the like.

The pressures applied to the subject at the locations of the firstsource-detector pair and the second source-detector pair are typicallyselected to be clinically acceptable. A pressure applied to a subject'scerebral region at the locations of the first and second source-detectorpairs is suitably in the range of from between about 0 and about 360torr. Separation (a) may suitably be in the range of from about 0.1 toabout 5 cm; separation (b) may also be in the range of from about 0.1 toabout 5 cm. Illumination may be light between 300 nm and 1500 nm inwavelength; one suitable typical wavelength range is between about 660and about 930 nm.

As described elsewhere herein, separations (a) and (b) may differ fromone another. (a) and (b) may be chosen such that detected illuminationfrom the longer of the two distances interrogates both layers when thehead of the subject is modeled as a two-layer medium comprising cerebraland extracerebral layers and detected illumination from one of the twoseparations interrogates the extracerebral layer.

Temporal changes in extracerebral flow and cerebral flow may be relatedto temporal changes in measured signal at the longer of (a) and (b) andmay be modeled via the Modified Beer Lambert Law applied to a two layermedium. The methods may be characterized as including diffusecorrelation spectroscopy, diffuse optical spectroscopy, diffusereflectance spectroscopy, or other techniques utilizing approximationsto the radiative transport equation. This method may be extended toadditional source-detector separations and layers (e.g., 5source-detector separations and 3 layers).

Also provided are methods, comprising: measuring a motion of movingscattering particles in a subject's tissue, the measuring comprisingilluminating the cerebral region and collecting illumination from afirst source-detector pair and with a second source-detector pair, thesource and detector of the first pair being separated by (a) a firstdistance and the source and detector of the second pair being separatedby (b) a second distance, the pressures applied to the subject's tissueat or proximate to the locations of the first source and the secondsource being different from one another, one or both of the pressuresbeing applied to as to induce variations in tissue hemodynamics, andisolating a tissue hemodynamic signal from the collected illumination.

A non-limiting listing of suitable tissues includes brain, muscle,and/or breast; brain is considered especially suitable as is pliablehealthy tissue overlying a mechanically stiff tumor. One of thepressures applied to the subject's tissue at the locations of the firstand second source-detector pairs is in the range of from about 0 toabout 360 torr. As described elsewhere herein, (a) may be in the rangeof from about 0.1 to about 5 cm, and (b) may be in the range of fromabout 0.1 to about 5 cm. Illumination may be illumination having awavelength of between about 300 nm and about 1500 nm. It should beunderstood that a user may use two, three, or even more source-detectorpairs to perform the disclosed methods and that likewise the discloseddevices may include two, three, four, or even more source-detectorpairs.

Separations (a) and (b) may differ from one another, and (a) and (b) maybe chosen such that detected illumination from the longer of the twodistances interrogates both layers when the tissue is modeled as atwo-layer medium that comprises tissue and extra-tissue layers anddetected illumination from one of the two separations interrogates theextra-tissue layer. Temporal changes in extra-tissue blood flow andtissue blood may be related to temporal changes in measured signal atthe longer of (a) and (b) modeled with the Modified Beer Lambert Law.The methods may be characterized as including diffuse correlationspectroscopy, diffuse optical spectroscopy, diffuse reflectancespectroscopy, or other techniques utilizing approximations to theradiative transport equation. Again, it should be understood thatalthough the foregoing discussion is focused on cerebral applications,the disclosed techniques may be generalized and applied to essentiallyany patient tissue.

Devices

As described elsewhere herein, Diffuse Correlation Spectroscopy (DCS) isa light scattering technique that measures CBF through the interactionof coherent light with moving particles. In practice, tissue (e.g., thehead) is illuminated with coherent laser light using fiber optics, andthe light scattered through the tissue (e.g., brain) is detected ˜2.5 cmaway on the surface of the head. Interaction of the scattered light withmoving particles in the blood (RBCs) causes the detected intensity tofluctuate in time. The characteristic time scale of these fluctuationsis a measure of CBF or other anatomical blood flow. More quantitatively,the temporal autocorrelation function of the detected intensity iscomputed and fit to a correlation diffusion equation to extract aquantitative and validated measure of CBF or other anatomical bloodflow. Because DCS is sensitive to all moving particles in the samplingarea, it is well-correlated with micro-vascular and parenchymal flow, asopposed to transcranial Doppler (TCD) measurements, which are sensitiveto large vessels.

An exemplary DCS instrument used in this study is shown in FIG. 3—left.The portable device consists of 2 long coherence length near infraredlasers (785 nm, Crystalaser) and 8 photon counting avalanche photodiodes(APD, Perkin Elmer), connected to flexible single mode fiber optics(Fiberoptic Systems Inc.). A built-in correlator (Correlator.com) readsthe photon counts from the APDs and computes the intensity correlationfunctions. Exemplary data acquisition and estimation of CBF was doneusing custom written software. In one study, flexible fiber optic probeswere attached to a patient's forehead with medical-grade adhesive andwere secured using soft elastic wraps around the head (FIG. 3—right).

Several approaches to a fiber probe skin interface are presented in oneDCS instrument. First, the illumination and detector fibers wereterminated with a 3 mm prism (Thorlabs, PS905), which improvedsignal-to-noise (SNR) by ˜3×. Additionally, multiple detector fiberswere terminated to a signal prism (and hence a single detectorposition), allowing for averaging of computed correlation curves tofurther improve signal-to-noise ratio. This design ensured that theprobe (FIG. 3—middle) was small, flexible and patient friendly.

Probes were manufactured using molds produced by 3D printing technology(Next Fab inc.), which enabled precise positioning of the prisms, andcontouring of the probes to fit the head curvature. FIG. 3's, middle andright figures show different exemplary probes; the probe in the middlepanel is a DCS probe that features two probe-detector separations. Theprobe in the right panel is a DCS/DOS probe that features four differentseparations. Finally, pressure sensors and accelerometers wereincorporated into the probe to enable robust measurement. Pressuremeasurements ensure proper and uniform probe-skin contact, whileaccelerometers help detect periods with motion artifacts.

In one non-limiting application of the disclosed technology, one mayapply the technology to analysis of stroke patients. The followingdiscussion is one non-limiting, exemplary use of the disclosedtechnology in a cerebral application.

Acute strokes are characterized by permanent damage to some portion ofthe brain—the ischemic core, and a surrounding region the penumbra wheredamage is reversible. The primary goal of stroke intervention techniquesis to increase cerebral blood flow in the brain, specifically in thepenumbra, to minimize damage.

Simple methods to increase CBF like lowering of the head of the patienthave shown measurable effects and clinical potential. Techniques likeadministration of hypertensive agents are not widely applicable and haveshown inconclusive results. An intravenous administration of salineincreases the fluid volume and hence CBF. The utility of this strokeintervention for patients with AIS is shown here using an improvedDCS/DOS device.

An illustrative study was approved by an Institutional Review Board ofthe Hospital of the University of Pennsylvania, and patients with AIS(acute ischemic stroke) (n=5) were recruited from the stroke unit at theHospital of the University of Pennsylvania. After obtaining informedconsent from patients, fiber optic probes were placed bilaterally at thetemporal margin of the forehead, superior to the frontal sinuses andsecured using medical grade adhesive tape (3M) and flexible cloth wrap.CBF was acquired continuously throughout the experiment using theDCS/DOS device. After a brief neurological exam, ˜15 minutes of baselineCBF measurements were collected, following which 500 cc of 0.9% NaCl wasintravenously administered for 30 mins. The experiment concluded with 15minutes of post-intervention measurements.

Preliminary results from this study were as follows. FIG. 6—left showsthe time course of % change in CBF during the course of an intravenousinjection of saline to a patient with a large left sided stroke. Thehemisphere contra-lateral to the injury shows an ˜40% increase in CBF,while the ipsi-lateral hemisphere shows a fairly small change in CBF.FIG. 6—right shows a summary of the average change in CBF in the contra-and ipsi-lateral hemispheres due to the saline bolus intervention in allpatients. The hemispherical asymmetries are apparent from this summary,with some patients even showing a decrease in CBF in the ipsi-lateralhemisphere. On average the change in CBF in the contralateral hemispherewas found to be 22%, while the change in CBF in the ipsilateral side is−1.5%.

Without being bound to any particular theory, one explanation for theheterogeneous results in FIG. 6—right is the vast differences in theextent of injury. For example, patient 1 had a severe stroke, whilepatients 3, 4, 5 had very mild symptoms. Again without being bound toany particular theory, it is possible that injury severity and stroketype have a significant effect on the CBF response to the saline bolusintervention. Thus, it was demonstrated that DCS can be used to monitorCBF changes during stroke intervention in patients with acute injury.Preliminary results show that an intravenous administration of normalsaline causes an increase in CBF in the hemisphere contralateral to theinjury.

As will be known to those of ordinary skill in the art, non-invasivediffuse optical measurements of tissue (e.g., cerebral) hemodynamicsdepend on stable positioning of light sources/detectors. However, it ischallenging for subjects to remain perfectly still (e.g., infants andchildren), and some paradigms such as HOB positioning involve deliberatemotion. Motional artifacts are important for photon correlation (DCS)measurements, because the resultant apparent movement of staticscatterers in tissue can cause additional signal decorrelation.Additionally, motional artifacts may lead to positional uncertainties,light leakage, and signal corruption that affect both DCS & DOS/NIRS.Experiments suggest that motion artifacts may also be considered incerebral measurements as well as in measurements of other parts of apatient's anatomy.

Accelerometers (e.g., motion sensors) may be integrated into the probesto continuously track the change in position of the patient's anatomyunder study (e.g., head). These devices measure acceleration along threeorthogonal axes. Optical measurements made in a clinical setting aresusceptible to artifacts arising from sudden motion by the subject.

Additionally, restless subjects may touch or adjust the probes,affecting both DOS and DCS measurements. Such motion artifacts are asignificant source of experimental noise in clinical measurements. Forblood flow measurements using DCS, this is especially significant, asthe technique is sensitive to all motion, not just that of blood.Although correlation decays can be separated out to some extent based onthe time scale of these artifacts, motion artifacts remain a significantchallenge during episodic occurrences like seizures or stammers, and inpediatric subjects. There is thus a necessity to develop techniques andmethods to remove the effect of motion artifacts. Thus, described hereinare devices that integrate an accelerometer into a probe that permitscontinuous recording of probe motion and thence automated detection ofmotion artifacts.

To understand patient motion, and its relation to measurements, one maywill track correlations between the time courses of CBF and netacceleration in a subject population. Time intervals wherein flow andmotion are highly correlated may be identified as periods of“significant motion” using a threshold identified from calibration teststudies. This filter may identify time-windows with potentially large‘artificial’ motion, may provide real-time feedback to the clinician ifsignificant movement is occurring, and may help select data withartifacts (in real-time and retrospectively).

Traditionally, DCS and DOS fibers have been physically separated intoseparate fiber optic bundles. The disclosed technology may, in someembodiments, co-locate single mode DCS detector fibers with multimodeDOS detector fibers into a single bundle with a single distal (skin) endand two proximal (detector) sub-bundles. Furthermore, one may alsosecure source fibers for DOS and DCS onto a single prism to couple lightinto the skin. Together, these improvements increase the overlap in thetissue volume probed by the two techniques.

Probes may also be built to: (1) improve physical and optical couplingthrough a range of head curvatures, (2) monitor pressure and motion, and(3) permit uniform pressure adjustment. One design terminates fiberswith a prism (e.g., Thorlabs, PS905). A detection fiber optic bundle mayinclude multi-mode fibers (44.6 nm-core/0.55 NA) for DOS/NIRS and singlemode fibers (5 nm−MFD/0.13 NA) for DCS, thereby facilitatingco-localized blood flow and oxygenation measurements. Coupling of lightthrough prisms reduces mechanical stress and increases light throughputat the skin-probe interface. With prism-coupled single-mode detectionfibers, one may observe ˜3× increases in SNR, which in turn enablesincreased source-detector separation distances that probe deeper intocortical tissues and improved temporal resolution.

Probes may conform to the anatomy of the patient, e.g., the varied heador chest curvatures of neonates to adults in the patient populations.One may manufacture a library of customized fiber optic probes withcurvatures corresponding to head circumferences ranging from 25 cm(premature babies) to 60 cm (adult) circumference, and one may use 3Dprinting (e.g., NextFab Studios, LLC) to produce the molds that shapethe probes. The process may include precision insets for theprism-couplers. A probe library may also be constructed for other partsof a patient's anatomy, e.g., to conform to a patient's chest or othermuscles.

To acquire data at different probe pressures, one may introduce flexiblepressure sensors (e.g., Tactilus Free Form, Sensor Products Inc.) intothe fiber optic probe (FIG. 3). Medical-grade double-sided tape ensuresproper probe contact and reduces skin-probe movement. To facilitatereal-time motion sensing, small, low power accelerometers (e.g., AnalogDevices ADXL335) may be embedded into the fiber optic probe duringmanufacture; the sensor and associated electrical connections will beheld in place above the prism-coupled fibers and elastomer will bepoured around it. Signals from the pressure and motion sensors arelogged onto a computer, and integrated into existing custom clinicalinstrument control software.

A schematic and photograph of an exemplary probe support and pressureadjustment system adapted for cerebral applications is shown in FIG. 3.The probe on each hemisphere may be held onto the head by severaltechniques, e.g., (1) a soft elastic strap wrapped around the head andover the probe; (2) or a pliable neoprene sheet, with an adjustablestrap. The elastic/adjustable straps wrap around the probe and head toset up a secure configuration. A hand inflatable air balloon (e.g.,American Diag. Corp, 875N) may be inserted between the probe and elasticstrap to permit systematic increase/decrease of probe pressure, whilemonitoring pressure via the embedded sensors. Pressure adjustments mayalso be mechanized under computer control.

Thus, the present disclosure provides devices, comprising: a firstillumination source-detector pair, the source and detector beingseparated by a first distance (a); a second illumination source-detectorpair, the source and detector being separated by a second distance (b);and an element configured to apply (or measure, or both) a pressurebetween the device and the subject's body. The devices may includeadditional source-detector pairs at the same or at additional distances.A device may also include an element (e.g., an accelerometer) configuredto measure acceleration or motion of the tissue being studied, thedevice being used, or both.

In some embodiments, at least one of the first and secondsource-detector pairs comprises optical fiber. An illumination source,an illumination detector, or both may be disposed within a bundle ofoptical fibers.

A device may further include an illumination element in electrical oroptical communication with the first, second, or both illuminationsource-detector probes. Such elements include a LASER (LightAmplification through Stimulated Emission of Radiation), a lamp, a lightemitting diode (LED), or any combination thereof.

The first illumination source, the first illumination detector, thesecond illumination source, the second illumination detector, or anycombination thereof may be in optical communication with a prism. Anillumination detector may be in optical communication with a prism.

As described elsewhere herein, separations (a) and (b) may differ fromone another. The first illumination source, the first illuminationdetector, the second illumination source, the second illuminationdetector, or any combination thereof, may be characterized as beingconformable to a patient's anatomy, e.g., by use of a flexible materialsuch as a plastic or mesh.

A device may also include an accelerometer. A user may use theaccelerometer to identify periods when the patient may have been moving,which in turn may be used to discard or discount data gathered duringperiods of motion.

A device may include a sensing element configured to measure pressurebetween a portion of the device and the patient's body (e.g., head). Theelement may be a balloon, a hydraulic element, a servo, or anycombination thereof. A device may also include, e.g., a photon countingavalanche diode, a photomultiplier tube (PMT), a photo diodes (PD), anavalanche photodiode (APD), a charge coupled device (CCD), acomplementary metal oxide semiconductor (CMOS), or any combinationthereof in electronic communication, optical communication, or both,with at least one of the first or second illumination detectors. Adevice may also include an element configured to compute intensitycorrelation functions from photon counts, the device being in electroniccommunication, optical communication, or both with a illuminationdetector probe.

A user may use the disclosed devices to measure a motion of movingscattering particles in a subject's tissue (e.g., blood components). Auser may further isolate tissue blood flow signals from collectedillumination. A user may also use the disclosed devices to apply apressure to a subject's body. A user may utilize the disclosed devicesto separate superficial (scalp) and underlying (cerebral) blood flow. Auser may utilize the disclosed devices to conduct long-term(hours-weeks) monitoring of tissue hemodynamics in a clinical oroutpatient setting.

FIG. 16 provides an exemplary device. As shown in that figure, a probemay include a housing that surrounds a set of optical components. In oneembodiment, the housing may include two larger cylinders concentric witha smaller cylinder. This shape permits the device (as a rigid orsemi-rigid body) to be integrated into a thin flexible sheet (e.g., arubber cap) to hold the probe close to the subject's head.

Several components may be within the housing. Such components may be,e.g., a fiber optic, a prism or mirror, a short optical component, and alens or other optical component that interfaces with the skin. Theinterfacing component may have rounded edges so as to interface morecomfortably with the skin.

Optical components may be physically fused together. Such components mayalso have optical coupling gel (Cargille and Thorlabs are consideredsuitable suppliers of such gels) between joints to provide freedom torotate and thus reduce breakage. Optical coupling gel may also be usedat the skin-device interface. In particular, this interface may utilizescattering optical coupling gel in order to minimize the number ofdiffuse-non-diffuse boundaries. The optical components and plastichousing may, in some embodiments, be assembled and/or created withadditive manufacturing in their final position.

The fiber optic of the disclosed devices may comprise a single fiber, abundle of similar fibers, or a bundle of dissimilar fibers. As describedelsewhere herein, one may include single mode fibers for diffusecorrelation spectroscopy measurements along with multimode fibers fordiffuse optical spectroscopy measurements.

FIG. 16 provides an exemplary device. As shown in that figure, a probemay include a housing that surrounds a set of optical components. In oneembodiment, the housing may include two larger cylinders concentric witha smaller cylinder. This shape permits the device (as a rigid orsemi-rigid body) to be integrated into a sheet or band (e.g., a rubbercap) to hold the probe close to the subject's head. In one exemplaryembodiment, the device includes a recess (shown) or protrusion (notshown) engages with a hole or other feature of a sheet, cap, or band soas to maintain the device in place. As shown in that figure, a devicemay include an optical lens that is in optical communication with afiber optic. As shown, the fiber optic may be a an individual fiber oreven a bundle of similar or dissimilar fibers.

Several components claim may be within the housing. Such components maybe, e.g., a fiber optic, a prism or mirror, a short optical component,and a lens or other optical component that interfaces with the skin. Theinterfacing component may have rounded edges so as to interface morecomfortably with the skin.

Optical components may be physically fused together. Such components mayalso have optical coupling gel between joints to provide freedom torotate and thus reduce breakage. The optical components and plastichousing may, in some embodiments, be assembled and/or created withadditive manufacturing in their final position.

The fiber optic of the disclosed devices may comprise a single fiber, abundle of similar fibers, or a bundle of dissimilar fibers. As describedelsewhere herein, one may include single mode fibers for diffusecorrelation spectroscopy measurements.

As shown in exemplary FIG. 16, a device may include an optical lens thatis in optical communication with a fiber optic. As shown, the fiberoptic may be a an individual fiber or even a bundle of fibers.

The device suitably includes a lens, as shown. The lens may be roundedor otherwise featured so as to more comfortable engage with the subject.The device may also include a feature (e.g., rounded projection) betweenthe lens and the subject. An optical element (e.g, lens, prism, mirror,fiber, and the like) may be present within the device so as to placevarious components into optical communication with one another.

The structural enclosure suitably contains various optical components ofthe devices. The enclosure may be cylindrical as shown in FIG. 16, butmay be of any configuration needed. The enclosure may have across-section in the range of from about 1 mm to about 50 mm, or in therange of from about 5 mm to about 25 mm. The devices may include aspring, elastomer, or other element configured to maintain pressurebetween the device and a subject.

Additional Disclosure, Simulations, and In Vivo Results

As described elsewhere herein, the Modified Beer-Lambert law forDOS/NIRS is readily derived from the first order Taylor expansion of theoptical density: OD≈OD⁰+(∂OD⁰/∂μ_(a))Δμ_(a)+(∂OD⁰/∂μ_(s)′)Δμ_(s)′,wherein the partial derivatives are evaluated in the “baseline” state(μ_(a)=μ_(a) ⁰,μ_(s)′=μ_(s)′⁰), OD⁰≡−log [I⁰/I_(s)] is the baselineoptical density, and the differential changes in absorption andscattering are denoted by Δμ_(a)≡μ_(a) ⁰(t)−μ_(a) ⁰ andΔμ_(s)′≡μ_(s)ζ(t)−μ_(s)ζ⁰, respectively. Note that the superscript “0”indicates baseline. Within this approximation, the change in opticaldensity is

$\begin{matrix}{{\Delta \; {OD}} = {{- {\log ( \frac{I(t)}{I^{0}} )}} \approx {{{\langle L\rangle}{{\Delta\mu}_{a}(t)}} + {( \frac{\mu_{a}^{0}}{\mu_{s}^{\prime 0}} ){\langle L\rangle}{{\Delta\mu}_{s}^{\prime}(t)}}} \approx {{\langle L\rangle}{{{\Delta\mu}_{a}(t)}.}}}} & (1)\end{matrix}$

Here,

L

≡∂OD⁰/∂μ_(a) is the so-called differential pathlength factor, which isapproximately the mean pathlength that diffusing photons travel fromsource to detector (i.e., through the medium). While the traditionalBeer-Lambert law relates absolute optical densities to absoluteabsorption coefficients, the Modified Beer-Lambert law (Eq. (1) in thissection of the disclosure) relates differential changes in the opticaldensity to differential changes in the absorption coefficient.

The method disclosed here provides a Modified Beer-Lambert law formeasurement of blood flow based on the DCS/DOS technique. The methodsrelate measured changes in a “DCS optical density” to changes in tissueblood flow, tissue scattering, and tissue absorption. Because thediffusion equation for the DCS signal, more specifically the so-calledcorrelation diffusion equation, is sensitive to the movement of redblood cells in tissue microvasculature, the disclosed methods differfrom previous efforts. This disclosure provides exemplary results formeasurement of flow changes in any geometry, including specificexpressions for two commonly used approximations for tissue models:homogeneous semi-infinite turbid media and two-layer turbid media. Thedisclosed approach is demonstrated by reference to simulations and an invivo experiment. The disclosed methods will lead to improvements incharacterization of cerebral flow and metabolism, with concomitantclinical impact.

Diffuse Correlation Spectroscopy

As mentioned elsewhere herein, diffuse correlation spectroscopy (DCS)uses NIR light to noninvasively measure tissue blood flow. The DCS bloodflow index has been successfully validated against a plethora of‘gold-standard’ techniques.

DCS detects tissue blood flow using speckle correlation techniques. Itmeasures the temporal intensity fluctuations of coherent NIR light thathas scattered from moving particles (red blood cells) in tissue (FIG.8A). These temporal fluctuations (FIG. 8B) are quantified by computingthe normalized intensity temporal auto-correlation function at multipledelay-times, i.e., one may compute g₂(τ)=

I(t)I(t+τ)

/

I(t)

², where I(t) is the intensity of the detected light, and the angularbrackets,

, represent time-averages. Formally, the transport of temporal fieldfluctuations through turbid media is modelled by the so-calledcorrelation diffusion equation, and the decay of the detectedautocorrelation function determines a tissue blood flow index (FIG. 8C).

The correlation diffusion equation models the transport of the electricfield auto-correlation function, G₁(τ)

E*(t)·E(t+τ)

, and it can be solved analytically or numerically for tissue geometriesof interest. The normalized electric field auto-correlation function,g₁(τ)=G₁(τ)/G₁(τ=0), is related to the measured (normalized) intensityauto-correlation function via the Siegert relation: g₂(τ)=1+β|g₁(τ)|²,where β is a constant determined primarily by the collection optics ofthe experiment.

As one example, for the simple case of point illumination and detectionof homogenous semi-infinite turbid media (FIG. 8A) with tissueabsorption coefficient μ_(a), tissue reduced scattering coefficientμ_(s)′, and tissue blood flow index F, the solution to the correlationdiffusion equation is:

$\begin{matrix}{{G_{1}(\tau)} = {{\frac{3}{4\pi \; _{tr}}\lbrack {\frac{\exp ( {{- {K(\tau)}}r_{1}} )}{r_{1}} - \frac{\exp ( {{- {K(\tau)}}r_{b}} )}{r_{b}}} \rbrack}.}} & (2)\end{matrix}$

Here, K(τ)=[3μ_(a)(μ_(a)+μ_(s)′)(1+2μ_(s)′k₀ ²Fτ/μ_(a))]^(1/2),r₁=(l_(tr) ²+ρ²)^(1/2), and r_(b)=[(2z_(b)+l_(tr))²+ρ²]^(1/2), wherein ρis the source detector separation and l_(tr)=1/(μ_(a)+μ_(s)′) is thephoton transport mean-free path through tissue. Further, k₀=2πn/λ is themagnitude of the light wave vector in the medium, andz_(b)=2l_(tr)(1+R_(eff))/(3(1−R_(eff)), where R_(eff) is the effectivereflection coefficient to account for the mismatch between the index ofrefraction of tissue (n) and the index of refraction of thenon-scattering medium bounding tissue (n_(out)), e.g., air.

One approach for blood flow monitoring with DCS in this geometry is toderive g₁(τ) from measurements of g₂(τ) via the Siegert relation. Then,the semi-infinite correlation diffusion solution (Eq. (2)) is fit usinga nonlinear minimization algorithm to g₁(τ) in order to obtain anestimate of the blood flow index.

Modified Beer-Lambert Law for Flow

Here is provided a “Modified Beer-Lambert law” for tissue blood flowbased on the DCS measurement. The first step in this process is todefine a DCS optical density (analogous to the DOS/NIRS OD). Forsource-detector separation ρ and delay-time τ, we define the DCS opticaldensity as: OD_(DCS)(τ,ρ)≡−log(g₂(τ,ρ)−1). In addition to delay time andsource-detector separation, the DCS optical density also implicitlydepends on tissue absorption, scattering, and blood flow (e.g, Eq. (2)in this section).

DCS Modified Beer-Lambert Law for Homogeneous Tissue

One may begin by deriving a general expression for homogeneous tissue,characterized by a blood flow index, F, an absorption coefficient,μ_(a), and a reduced scattering coefficient, μ_(s)′. The DCS ModifiedBeer-Lambert law is derived by truncating the Taylor series expansion ofthe DCS optical density to first order in F, μ_(a), and μ_(s)′, i.e.,

$\begin{matrix}{{{OD}_{DCS}( {\tau,\rho} )} \approx {{{OD}_{DCS}^{0}( {\tau,\rho} )} + {\frac{\partial{OD}_{DCS}^{0}}{\partial F}\Delta \; F} + {\frac{\partial{OD}_{DCS}^{0}}{\partial\mu_{a}}\Delta \; \mu_{a}} + {\frac{\partial{OD}_{DCS}^{0}}{\partial\mu_{s}^{\prime}}\Delta \; {\mu_{s}^{\prime}.}}}} & (3)\end{matrix}$

Here, OD_(DCS) ⁰(τ,ρ)≡−log(g₂ ⁰(τ,ρ)−1) is the “baseline” (i.e., timet=0) DCS optical density with a baseline blood flow index F⁰ and withbaseline optical properties μ_(a) ⁰ and μ_(s)′⁰. Correspondingly,OD_(DCS)(τ,ρ)≡−log(g₂(τ,ρ)−1) is the DCS optical density for theintensity auto-correlation function in the “perturbed” state (i.e., timet) with blood flow index F and with optical properties μ_(a) and μ_(s)′.Hence, the differential changes from baseline of tissue blood flow,absorption, and scattering are ΔF≡F−F⁰, Δμ_(a)≡μ_(a)−μ_(a) ⁰, andΔμ_(s)′≡μ_(s)′−μ_(s)′₀, respectively.

Comparing Eq. (3) from this section with Eq. (1) from this section, theDCS analogues of the differential pathlength are d_(F)(τ,ρ)≡∂OD_(DCS)⁰/∂F, d_(a)(τ,ρ)≡∂OD_(DCS) ⁰/∂μ_(a), and d_(s)(τ,ρ)≡∂OD_(DCS) ⁰/∂μ_(s)′,which can be estimated analytically or numerically with the correlationdiffusion model applied to the appropriate geometry (see Appendix 1below). All three of these weighting factors depend on τ and ρ, ontissue geometry, and on the baseline parameters F⁰, μ_(a) ⁰, andμ_(s)′⁰. Rearranging Eq. (3) from this section, we arrive at the DCSModified Beer-Lambert law for homogeneous tissue:

$\begin{matrix}{{\Delta \; {{OD}_{DCS}( {\tau,\rho} )}} = {{- {\log ( \frac{{g_{2}( {\tau,\rho} )} - 1}{{g_{2}^{0}( {\tau,\rho} )} - 1} )}} \approx {{{d_{F}( {\tau,\rho} )}\Delta \; F} + {{d_{a}( {\tau,\rho} )}\Delta \; \mu_{a}} + {{d_{s}( {\tau,\rho} )}\Delta \; {\mu_{s}^{\prime}.}}}}} & (4)\end{matrix}$

Without being bound to any single theory, if the blood flow and opticalproperties change only slightly, then the perturbation in the DCSoptical density is small and the first order expansion (Eq. (3)) is agood approximation. Again without being bound to any single theory,larger tissue hemodynamic changes, ΔOD_(D), can still be small for shortdelay-times. In this limit, d_(F), d_(a), and d_(s) are typically small(FIG. 9). Analytical and numerical computation of the weighting factors(d_(F), d_(a), d_(s)) is described in Appendix 1 below.

Eq. (4) is a general, non-limiting result that describes the change inDCS optical density for homogeneous tissue. For a giventissue/measurement geometry, the change in blood flow may be computed byevaluating the weighting factors for the geometry in question, and thensubstituting in for them in Eq. (4).

DCS Modified Beer-Lambert Law for Homogeneous Semi-Infinite Geometry

One may evaluate weighting factors in Eq. (4) for the special case ofthe homogeneous semi-infinite geometry (FIG. 8). From Eq. (2), thenormalized electric field auto-correlation function is

$\begin{matrix}{{{g_{1}( {\tau,\rho} )} = \frac{{{\exp ( {{- {K(\tau)}}r_{1}} )}/r_{1}} - {{\exp ( {{- {K(\tau)}}r_{b}} )}/r_{b}}}{{{\exp ( {{- K_{0}}r_{1}} )}/r_{1}} - {{\exp ( {{- K_{0}}r_{b}} )}/r_{b}}}},} & (5)\end{matrix}$

where K(τ), r₁, and r_(b) are as defined in Section 2, andK₀=K(τ=0)=[3μ_(a)(μ_(a)+μ_(s)′)]^(1/2). The multiplicative weightingfactors in the semi-infinite geometry can be computed from substitutingEq. (5) into Eqs. (11) and (12), e.g.,

$\begin{matrix}{{d_{F}( {\tau,\rho} )} = {{\frac{6{\mu_{s}^{\prime 0}( {\mu_{s}^{\prime 0} + \mu_{a}^{0}} )}k_{0}^{2}\tau}{K^{0}(\tau)}\lbrack \frac{{\exp ( {{- {K^{0}(\tau)}}r_{1}^{0}} )} - {\exp ( {{- {K^{0}(\tau)}}r_{b}^{0}} )}}{{{\exp ( {{- {K^{0}(\tau)}}r_{1}^{0}} )}/r_{1}^{0}} - {{\exp ( {{- {K^{0}(\tau)}}r_{b}^{0}} )}/r_{b}^{0}}} \rbrack}.}} & (6)\end{matrix}$

In FIG. 9, d_(F), d_(a), and d_(s) for the semi-infinite geometry areplotted as a function of using typical tissue properties. The threeweighting factors are smaller in magnitude for shorter delay-times. Theweighting factor for absorption is negative, i.e., an increase inabsorption shifts the intensity auto-correlation function to the right(compared to baseline), and vice versa for increases in flow andscattering.

Because the weighting factors are smaller at shorter delay-times (FIG.9), the DCS optical density perturbation will also be smaller, which inturn means higher accuracy in the DCS Modified Beer-Lambert law (Eq.(4)). In the semi-infinite geometry, the delay-times used for Eq. (4)should satisfy the limits 2μ_(s)′k₀ ²Fτ/μ_(a)□1 and 2μ_(s)′⁰k₀²F⁰τ/μ_(a) ⁰□1 for the most quantitatively accurate results (seeAppendix 2 below). One exemplary, non-limiting “rule of thumb” foraccurately using Eq. (4) is to utilize data wherein g₁ ⁰(τ)>0.5.

FIG. 9B shows that for the same fractional changes (10%) in flow,scattering, and absorption, the change in DCS optical density isgreatest due to scattering, followed by flow; changes in absorption hadthe least influence on the DCS signal. In practice, concurrentfrequency-domain or time-domain NIRS/DOS may be employed to directlymeasure tissue absorption and scattering and account for their effects(i.e., if these parameters change). Note however, tissue scatteringchanges that accompany hemodynamic concentration variation are oftennegligible, since the origin of tissue scattering is predominantly frominterfaces between cells and the extracellular space or between cellularcytoplasm and cellular organelles.

DCS Modified Beer-Lambert Law for Heterogeneous Geometries

Tissue may be approximated to be optically homogeneous for hemodynamicmonitoring; this approach has the advantage of simplicity. Consideringtissue as heterogeneous, the tissue contains multiple compartments withdifferent optical properties due to blood vessels, fat, and bone. Theseregions can be modeled as “layers” below the tissue surface such asscalp, skull and cortex.

Under these conditions, one may use a Taylor series expansion of the DCSoptical density to derive the DCS Modified Beer-Lambert law forheterogeneous media. Assuming for purposes of explanation that theheterogeneous tissue can be discretized into N homogeneous regions, thefirst-order Taylor series expansion is

$\begin{matrix}{{{OD}_{DCS}( {\tau,\rho} )} \approx {{{OD}_{DCS}^{0}( {\tau,\rho} )} + {\sum\limits_{k = 1}^{N}\; {\lbrack {{\frac{\partial{OD}_{DCS}^{0}}{\partial F_{k}}\Delta \; F_{k}} + {\frac{\partial{OD}_{DCS}^{0}}{\partial\mu_{a,k}}\Delta \; \mu_{a,k}} + {\frac{\partial{OD}_{DCS}^{0}}{\partial\mu_{s,k}^{\prime}}\Delta \; \mu_{s,k}^{\prime}}} \rbrack.}}}} & (7)\end{matrix}$

Here, F_(k), μ_(a,k), and μ_(s,k)′ denote the blood flow index, tissueabsorption, and tissue scattering for the k^(th) homogeneous region inthe tissue, respectively, and ΔF_(k)≡F_(k)−F_(k) ⁰,Δμ_(a,k)≡μ_(a,k)−μ_(a,k) ⁰, and Δμ_(s,k)′≡μ_(s,k)′−μ_(s,k)′⁰ denote thechanges in these parameters from baseline.

Rearranging Eq. (7), the DCS Modified Beer-Lambert law for heterogeneousmedia is:

$\begin{matrix}{{{- {\log ( \frac{{g_{2}( {\tau,\rho} )} - 1}{{g_{2}^{0}( {\tau,\rho} )} - 1} )}} \approx {\sum\limits_{k = 1}^{N}\; \lbrack {{{d_{F,k}( {\tau,\rho} )}\Delta \; F_{k}} + {{d_{a,k}( {\tau,\rho} )}{\Delta\mu}_{a,k}} + {{d_{s,k}( {\tau,\rho} )}{\Delta\mu}_{s,k}^{\prime}}} \rbrack}},} & (8)\end{matrix}$

where {d_(F,k)≡∂OD_(DCS) ⁰/∂F_(k), d_(a,k)≡∂OD_(DCS) ⁰/∂μ_(a,k),d_(s,k)≡∂OD_(DCS) ⁰/∂μ_(s,k)′}, are DCS analogues of the partialpathlengths from DOS/NIRS. These multiplicative weighting factors dependon tissue geometry, on the baseline tissue properties, i.e., {F_(k) ⁰,μ_(a,k) ⁰, μ_(s,k)′⁰}, and on τ and ρ. They account for the relativeimportance of the various regional hemodynamic changes in the DCSoptical density perturbation, and they can be estimated in the samemanner as described in Appendix 1 herein.

Modified Beer-Lambert Law for Two-Layer Media

The simplest heterogeneous model for tissue is the two-layer geometry,which is an important special case (FIG. 10). For cerebral applications,the two-layer geometry is comprised of a semi-infinite bottom layer(i.e., corresponding to the cortical regions of the brain) with adistinct blood flow index, absorption coefficient, and scatteringcoefficient of F_(c), μ_(a,c) and μ_(s,c)′, respectively, and asuperficial top layer (i.e., corresponding to extra-cerebral scalp andskull tissue) with thickness, l, and distinct tissue properties denotedby F_(ec), μ_(a,ec), and μ_(s,ec)′.

The two-layer DCS Modified Beer-Lambert law is the special case of Eq.(8) for N=2 homogeneous regions, i.e.,

$\begin{matrix}{{\Delta \; {{OD}_{DCS}( {\tau,\rho} )}} = {{- {\log ( \frac{{g_{2}( {\tau,\rho} )} - 1}{{g_{2}^{0}( {\tau,\rho} )} - 1} )}} \approx {{{d_{F,c}( {\tau,\rho} )}\Delta \; F_{c}} + {{d_{F,{ec}}( {\tau,\rho} )}\Delta \; F_{ec}} + {{d_{a,c}( {\tau,\rho} )}{\Delta\mu}_{a,c}} + {{d_{a,{ec}}( {\tau,\rho} )}{\Delta\mu}_{a,{ec}}} + {{d_{s,c}( {\tau,\rho} )}{\Delta\mu}_{s,c}^{\prime}} + {{d_{s,{ec}}( {\tau,\rho} )}{{\Delta\mu}_{s,{ec}}^{\prime}.}}}}} & (9)\end{matrix}$

Again, the multiplicative weighting factors d_(F,i)≡∂OD_(DCS) ⁰/∂F_(i),d_(a,i)≡∂OD_(DCS) ⁰/∂μ_(a,i), and d_(s,i)≡∂OD_(DCS) ⁰/∂μ_(s,i)′ (withsubscript i denoting c (cerebral) or ec (extra-cerebral)), indicate therelative sensitivity of the DCS optical density to cerebral versusextra-cerebral hemodynamic changes. The parameters depend on delay-timeτ, source-detector separation ρ, extra-cerebral layer thickness e, andbaseline tissue properties F_(c) ⁰, F_(ec) ⁰, μ_(a,c) ⁰, μ_(a,ec) ⁰,μ_(s,c)′⁰, and μ_(s,ec)′⁰. They can be computed by numerically takingthe appropriate derivatives of the two-layer solution to the correlationdiffusion equation:

$\mspace{20mu} {{{g_{1}(\tau)} = {{G_{1}(\tau)}/{G_{1}(0)}}},\mspace{20mu} {{G_{1}(\tau)} = {\frac{1}{2\pi}{\int_{0}^{\infty}{(\tau){{sJ}_{0}( {s\; \rho} )}\ {s}}}}},{{(\tau)} = {{\frac{\sinh \lbrack {\kappa_{ec}( {z_{b} + z_{0}} )} \rbrack}{D_{ec}\kappa_{ec}}\frac{{D_{ec}\kappa_{ec}{\cosh \lbrack {\kappa_{ec}l} \rbrack}} + {D_{c}\kappa_{c}{\sinh \lbrack {\kappa_{ec}l} \rbrack}}}{{D_{ec}\kappa_{ec}{\cosh \lbrack {\kappa_{ec}( {l + z_{b}} )} \rbrack}} + {D_{c}\kappa_{c}{\sinh \lbrack {\kappa_{ec}( {l + z_{b}} )} \rbrack}}}} - \frac{\sinh \lbrack {\kappa_{ec}z_{0}} \rbrack}{D_{ec}\kappa_{ec}}}},}$

where D_(i)=1/[3(μ_(s,i)′+μ_(a,i))], κ_(i)²=(D_(i)s²+μ_(a,i)+2μ_(s,i)′k₀ ²F_(i)τ)/D_(i),z_(b)=D_(ec)(1±R_(eff))/(1−R_(eff)), z₀=3D_(ec), and R_(eff) and k₀ aredefined as set forth elsewhere herein. For illustration purposes, thissolution assumes that the top and bottom layers are (refractive)index-matched. The two-layer weighting factors for a typical set ofextra-cerebral/cerebral tissue properties are plotted in FIG. 11.Importantly, for a source-detector separation ρ=3 cm, the change in theDCS optical density is more sensitive to changes in flow and absorptionin the cerebral layer rather than in the extra-cerebral layer (exceptfor very long delay-times). This sensitivity is especially prominent atthe shorter delay-times (FIGS. 11B, 11C). These differences may arisebecause of the difference in magnitude of cerebral versus extra-cerebralflow (e.g., cerebral flow is approximately 10 times faster thanextra-cerebral flow).

The increase in the influence of the extra-cerebral layer at longerdelay times (FIG. 11C) may be explained by consideration of thepathlengths of light and their association with short versus longcorrelation decay times T. Briefly, in the auto-correlation decayfunction, long light paths contribute rapid decays to the signal (shortτ) and short light paths contribute slow decays to the signal (large τ).At short source-detector separations, e.g., ρ=0.5 cm, which mostlysample the superficial layer, the DCS optical density perturbation ispredominantly sensitive to the superficial layer (FIG. 11C). Inagreement with Selb et al, a comparison of FIGS. 11C and 11D revealsthat the DCS optical density is more sensitive to cerebral changes thanthe DOS/NIRS optics density. Again, this is largely because cerebralblood flow is much greater than extra-cerebral blood flow, and becauseDCS is effectively a time resolved technique that permits separation oflong light paths (shorter delay-times) from short light paths (longerdelay-times).

Validation with Simulated Data

The semi-infinite DCS Modified Beer-Lambert law (Eq. (4)) was testedusing simulated data (FIG. 12). The simulated DCS data was generatedfrom semi-infinite analytical solutions of the correlation diffusionequation (Eq. (5)) with added noise. Baseline tissue blood flow andoptical properties in the simulated data were chosen to berepresentative of the head, and perturbations from baseline were inducedby varying blood flow (F) from +50% to −50%, with constant tissueoptical properties. FIG. 12A shows the simulated intensityauto-correlation functions for these baseline and perturbed conditions,plotted as a function of delay-time. The DCS Modified Beer-Lambert law(Eq. (4)) was applied to this simulated data set to calculate the flowchange as a function of delay-time (FIG. 12B). There is good agreementbetween the calculated and actual flow changes for a wide range ofdelay-times.

To quantify this range of delay-times for which the DCS ModifiedBeer-Lambert law can be accurately employed, the semi-infinite DCSModified Beer-Lambert law is expected to be accurate in the limit2μ_(s)′k₀ ²Fτ/μ_(a)□1 (Appendix 2 below). Modeling shows that it willremain fairly accurate even when 2μ_(s)′k₀ ²Fτ/μ_(a)˜1. To appreciatethe simulation results more generally, we introduce the dimensionlessdelay-time, τγ⁰F⁰, which depends on baseline blood flow)(F⁰),correlation time-delay (τ), and γ⁰≡K₀ ⁰(μ_(s)′⁰/μ_(a) ⁰)k₀ ²r₁ ⁰ (Eq.(17)); when this dimensionless delay-time is ˜1, the baseline fieldcorrelation function has decayed by ˜1/e. In terms of this dimensionlessdelay-time, the limit 2μ_(s)′k₀ ²Fτ/μ_(a)□1 corresponds to the baselinecondition τγ⁰F⁰□α, where α≡γ⁰μ_(a) ⁰/(2μ_(s)′⁰k₀ ²). For the “typical”conditions chosen for FIG. 12, α=2.34.

FIG. 12B indicates the difference (error) between the calculated DCSModified Beer-Lambert flow change (estimated for each dimensionlessdelay-time) and the true flow change (simulated value). This error isrelatively small, even for dimensionless delay-times approaching α=2.34.Once the auto-correlation curves are close to fully decayed, the DCSModified Beer-Lambert law is predominantly sensitive to correlationnoise instead of flow changes. For a perturbed state from baseline(e.g., rbf=50%), the limit 2μ_(s)′k₀ ²Fτ/μ_(a)□1 corresponds toτγ⁰F⁰□α(F⁰/F) (assuming constant optical properties). The greater F is,the smaller the upper limit on the dimensionless delay-time time willbe.

Noise Consideration

At very short delay-times, there is little difference between theintensity auto-correlation curves at different blood flows (FIG. 12A).Consequentially, the changes to the DCS optical density in this limitare heavily influenced by correlation noise. Hence the flow calculationsat the very short delay-times in FIG. 12B are noisy. In general, fromapplying error propagation rules to Eq. (4), the noise in the calculatedflow change as a function of τ for constant tissue optical properties is

$\begin{matrix}{{\delta ( {{rbf}(\tau)} )} = {{\frac{1}{{d_{F}(\tau)}F_{0}}{\delta ( {\Delta \; {{OD}_{DCS}(\tau)}} )}} = {\frac{1}{{d_{F}(\tau)}F_{0}}{\frac{\delta ( {{g_{2}(\tau)} - 1} )}{{{g_{2}(\tau)} - 1}}.}}}} & (10)\end{matrix}$

A correlation noise model can be used to accurately model δ(g₂(τ)−1). Asτ increases, the correlation noise decreases and d_(F)(τ)F₀ increases(FIG. 9A). Both of these trends reduce the noise in rbf. However, when|g₂(τ)−1| goes to zero as τ increases, a concurrent increase in noise isexpected. From FIG. 12B, the noise in rbf falls with increasingdelay-time and then levels off around τγ⁰F⁰≈0.3; the noise then remainsconstant for a large range of delay-times.

As one would expect, the flow change computed with a single τ in the DCSModified Beer-Lambert law is more sensitive to correlation noise thanthe flow change extracted from nonlinear fits to the semi-infinitecorrelation diffusion solution across many delay-times (see FIGS. 13,14). To reduce sensitivity to noise, multiple delay-times can also beused for the DCS Modified Beer-Lambert law. Eq. (4) then becomes asystem of linear equations; one equation for each delay-time, which canvery rapidly be solved for the flow change.

In Vivo Validation

The semi-infinite DCS Modified Beer-Lambert law was also validated invivo on a juvenile pig (FIGS. 13-14). The scalp of the juvenile pig wasreflected and 2.5-mm burr holes were drilled through the skull down tothe dura. Optical fibers were inserted into the holes to form one DCSsource-detector pair to measure cerebral blood flow and one NIRSsource-detector pair to measure cerebral tissue absorption. Thesource-detector separations of both pairs were approximately 1.5 cm, andthe baseline cerebral optical properties of the pig were assumed to beμ_(a) ⁰(785 nm)=0.2 cm⁻¹ and μ_(s)′⁰(785 nm)=8 cm⁻¹. In thismeasurement, the semi-infinite geometry is a good approximation of thetissue geometry because the optical fibers are very close to the brain.

A 200% increase in cerebral blood flow was induced in the pig via venousinfusion of 9 mg/kg of the drug dinitrophenol (DNP). DNP is a protontransporter across cell membranes, which disrupts the mitochondrialproton gradient. In an effort to restore the proton gradient, cellsheavily stimulate cerebral oxygen metabolism, which in turn leads to alarge increase in cerebral blood flow.

The calculated temporal cerebral blood flow changes in the pig from DNPusing the DCS Modified Beer-Lambert law are in good agreement with thecalculated changes from nonlinear fits to the semi-infinite solution ofthe correlation diffusion equation (FIG. 13). Measured cerebralabsorption changes (FIG. 14B) were incorporated in the blood flowcalculations. Note that when using multiple delay-times in the DCSModified Beer-Lambert law, the noise in temporal blood flow estimates iscomparable to the nonlinear diffusion fit (FIG. 13A). For single τ bloodflow monitoring, the temporal blood flow noise is larger, but theaverage blood flow changes are the same (FIG. 13B), which demonstratesthe feasibility of accurate single τ blood flow monitoring with DCS. InFIG. 13B, τγ⁰F⁰=0.33 (corresponding to g₂ ⁰(τ)=1.30) was used for singledelay-time monitoring.

The estimated cerebral blood flow changes in the pig from the DCSModified Beer-Lambert law are also plotted as a function ofdimensionless delay-time in FIG. 14A for two quasi steady-state temporalintervals. During these temporal flow intervals, the blood flow changeswere also determined from nonlinear fits to the semi-infinitecorrelation diffusion solution. The average blood flow changes from thenonlinear fit estimates are 185% and 64% (solid black lines). Thehorizontal dashed lines in FIG. 14A indicate the noise in the nonlinearfit estimates of blood flow (constant because the nonlinear correlationdiffusion fit uses all delay-times). Interestingly, although estimatesof blood flow changes obtained from the DCS Modified Beer-Lambert laware noisy, the average value of these estimates are within the noise ofthe nonlinear correlation diffusion fit estimates for the delay-timeinterval 0.16<τγ⁰F⁰<0.82, which corresponds to the baseline intensityauto-correlation function range 1.15<g₂ ⁰(τ)<1.40.

DISCUSSION

This disclosure extends a new approach to DCS measurement anddemonstrates the accuracy of this extension in both simulations (FIG.12) and in vivo data (FIGS. 13, 14). As with the Modified Beer-Lambertapproach, the DCS Modified Beer-Lambert approach has advantages comparedto the traditional approach of fitting intensity auto-correlation datato nonlinear solutions of the correlation diffusion equation.

Real-Time Estimates of Blood Flow Changes

The DCS Modified Beer-Lambert law is a linear equation relating changesin blood flow to changes in signal for any tissue geometry. Although thecorrelation diffusion solution in the semi-infinite geometry is closedform, the correlation diffusion solutions in more intricate geometries(e.g., curved, layered) are vastly more complex, and consequentiallyquite time-consuming when fitting data. With the DCS ModifiedBeer-Lambert approach, the correlation diffusion solutions are neededonly once, in order to evaluate the multiplicative weighting factors atthe “baseline” tissue state, e.g., Eq. (13). Then, blood flow changesfrom baseline are rapidly determined by solving a linear equation (Eq.(4) or (8)). Consequentially, the DCS Modified Beer-Lambert law is wellsuited for real-time blood flow monitoring, especially in tissuegeometries that are not semi-infinite.

Blood Flow Monitoring in Tissues Wherein Light Propagation isNon-Diffusive

Diffusive light transport is not required for using the DCS ModifiedBeer-Lambert approach. In blood flow monitoring applications wherein thephoton diffusion model is not valid, the multiplicative weightingfactors can be evaluated using solutions to the correlation transportequation instead of the correlation diffusion equation (see Appendix 1).For the tissue geometry of interest, the correlation transport equationcan be solved numerically with Monte Carlo techniques. Thus, the DCSModified Beer-Lambert approach facilitates accurate blood flowmonitoring for the small source-detector separations typical ofendoscopic probes or speckle correlation based imaging methods, forcomplex tissues that contain “non-diffusing” domains such as (arguably)cerebral spinal fluid inside the head, and for tissues that contain veryhigh concentrations of blood, as in the liver. In all three of theseexamples, the assumptions underlying the photon diffusion model areviolated, and therefore the photon diffusion model is not expected to beaccurate. Another potential application of the non-diffusive DCSModified Beer-Lambert approach is blood flow monitoring with visiblelight.

Improved Depth Sensitivity

The DCS Modified Beer-Lambert law permits blood flow monitoring withintensity auto-correlation measurements at a single delay-time, incontrast to the traditional correlation diffusion approach wherein bloodflow estimates are obtained by acquiring and fitting a full intensityauto-correlation curve consisting of many delay-times. It has been wellestablished that the auto-correlation function decay times of long lightpaths are relatively short, while the decay times of short paths arerelatively long. Thus, the auto-correlation function at shorterdelay-times will inherently be more sensitive to deeper tissues (FIG.11), which in turn means that the sensitivity of the DCS measurement toblood flow at deeper tissue depths is improved by using shortdelay-times in the DCS Modified Beer-Lambert law. Conversely, using longdelay-times improves the sensitivity of the DCS measurement to tissueblood flow at shallow depths. This same effect can be achieved byfitting different parts of the intensity auto-correlation curve to thecorrelation diffusion model. In practice, these correlation diffusionfits still require several delay-times spanning a significant portion ofthe auto-correlation curve. By using one delay-time, the experimenterhas finer control of the measurement depth sensitivity.

Fast DCS Measurement Speed

Importantly, the DCS Modified Beer-Lambert law offers new routes forincreased DCS measurement speed and for simpler instrumentation.Underlying these advantages is again the aspect of blood flow monitoringwith a single delay-time. We and others have used multiple-tau hardwarecorrelators to measure the intensity auto-correlation function atdelay-times spanning several orders of magnitude from 100 ns to 10 ms.Achieving sufficient SNR for deep tissue DCS measurements (e.g., as inthe brain) typically requires averaging many (N>100) of these 10-msauto-correlation curves. The single delay-time cerebral blood flowmonitoring in the pig shown in FIG. 13B was done at r=3.8 μs. Thus, inthis example, ˜250 blood flow measurements can be acquired in 1 ms,which can then be temporally averaged to reduce noise. In 10 ms, whichis roughly the time required to measure a single auto-correlation curvewith a multiple τ correlator, 2500 blood flow measurements can beacquired and averaged. Therefore, even though single τ blood flowmonitoring with the DCS Modified Beer-Lambert law is more sensitive tocorrelation noise than multiple τ monitoring (FIGS. 13-14), thesubstantial improvement in the blood flow sampling rate with single τmonitoring means that enough averaging can be employed to compensate forthis additional noise while still maintaining high DCS measurementspeeds. Blood flow measurements at high acquisition rates areadvantageous in several applications, including schemes to filter outmotion artifacts in exercising muscle. Single τ monitoring also makes itpossible to use single τ hardware correlators, which are cheaper thanmultiple τ hardware correlators. Alternatively, software correlators fora single delay-time can be implemented.

Filtering Out Contamination from Superficial Tissues in Deep Tissue FlowMonitoring

Paradigms developed with the Modified Beer-Lambert law to filter outcontamination from superficial tissues in blood oxygenation measurementsof the tissue of interest (e.g., the brain) can be used in the DCSModified Beer-Lambert formulation for blood flow monitoring.

One scheme for filtering out superficial tissue contamination in the DCSsignal is to use two source-detector separations, one of which is longand the other short. Detected light from the long separation travelsthrough both layers of tissue, but detected light at the shortseparation is predominantly confined to the superficial layer. The twosource-detector separation DCS Modified Beer-Lambert law can be employedto isolate the deep tissue blood flow component in the DCS signal fromthe superficial blood flow component by acquiring “initial/baseline”measurements wherein only superficial blood flow is changing. Incerebral monitoring, one way to change superficial blood flow withoutaffecting cerebral blood flow is to vary the pressure of the opticalprobe against the head. Thus, initial measurements acquired during probepressure modulation can be used to derive the patient-specific weightingfactors in the two source-detector separation DCS Modified Beer-Lambertlaw. These weighting factors are then used to filter out superficialcontamination in subsequent cerebral blood flow monitoring.

Low Sensitivity of Blood Flow Monitoring to “Baseline” Tissue Properties

Implementing the DCS Modified Beer-Lambert law requires knowledge of thebaseline tissue properties to evaluate the multiplicative weightingfactors. These baseline tissue properties can either be assumed from theliterature (e.g.,) or measured with time-domain or frequency-domainNIRS. For typical tissue measurements, the sensitivity in the computedfractional blood flow change to assumed baseline optical properties issmall (FIG. 15). Thus, for many applications, errors in the assumedbaseline optical properties has little effect on calculated changes inblood flow.

Appendix 1

The multiplicative weighting factors d_(F), d_(a), and d_(s) in Eq. (4)can be estimated by taking the appropriate derivative of the solutionsto the correlation diffusion equation applied to the appropriategeometry (e.g., semi-infinite homogeneous, etc.). First, using theSiegert relation, we have:

$\begin{matrix}\begin{matrix}{{{d_{F}( {\tau,\rho} )} \equiv {\frac{\partial}{\partial F}\lbrack {- {\log ( {{g_{2}^{0}( {\tau,\rho} )} - 1} )}} \rbrack}} = {\frac{\partial}{\partial F}\lbrack {{- \log}( {\beta \lbrack {g_{1}^{0}( {\tau,\rho} )} \rbrack}^{2} )} \rbrack}} \\{= {{\frac{\partial}{\partial F}\lbrack {{- {\log (\beta)}} - {\log ( \lbrack {g_{1}^{0}( {\tau,\rho} )} \rbrack^{2} )}} \rbrack} = {2{{\frac{\partial}{\partial F}\lbrack {- {\log ( {g_{1}^{0}( {\tau,\rho} )} )}} \rbrack}.}}}}\end{matrix} & (11)\end{matrix}$

Similarly,

$\begin{matrix}{{{d_{a}( {\tau,\rho} )} = {2{\frac{\partial}{\partial\mu_{a}}\lbrack {- {\log ( {g_{1}^{0}( {\tau,\rho} )} )}} \rbrack}}},{{d_{s}( {\tau,\rho} )} = {2{{\frac{\partial}{\partial\mu_{s}^{\prime}}\lbrack {- {\log ( {g_{1}^{0}( {\tau,\rho} )} )}} \rbrack}.}}}} & (12)\end{matrix}$

Here, g₁(τ,ρ) is the solution to the correlation diffusion equation forthe geometry of interest, and the derivatives of the solution areevaluated at baseline conditions. In conditions where an analyticalsolution for the correlation diffusion equation does not exist, themultiplicative weighting factors can be computed numerically:

$\begin{matrix}{{{d_{F}( {\tau,\rho} )} = {\frac{2}{\Delta \; F}{\log ( \frac{g_{1}( {\tau,\rho,{( {F^{0} - {\Delta \; F}} )/2},\mu_{a}^{0},\mu_{s}^{\prime 0}} )}{g_{1}( {\tau,\rho,{( {F^{0} + {\Delta \; F}} )/2},\mu_{a}^{0},\mu_{s}^{\prime 0}} )} )}}},{{d_{a}( {\tau,\rho} )} = {\frac{2}{\Delta \; \mu_{a}}{\log ( \frac{g_{1}( {\tau,\rho,F^{0},{( {\mu_{a}^{0} - {\Delta\mu}_{a}} )/2},\mu_{s}^{\prime 0}} )}{g_{1}( {\tau,\rho,F^{0},{( {\mu_{a}^{0} + {\Delta\mu}_{a}} )/2},\mu_{s}^{\prime 0}} )} )}}},{{d_{s}( {\tau,\rho} )} = {\frac{2}{\Delta \; \mu_{s}^{\prime}}{\log ( \frac{g_{1}( {\tau,\rho,F^{0},\mu_{a}^{0},{( {\mu_{s}^{\prime 0} - {\Delta\mu}_{s}^{\prime}} )/2}} )}{g_{1}( {\tau,\rho,F^{0},\mu_{a}^{0},{( {\mu_{s}^{\prime 0} + {\Delta\mu}_{s}^{\prime}} )/2}} )} )}}},} & (13)\end{matrix}$

where ΔF/F⁰=Δμ_(a)/μ_(a) ⁰=Δμ_(s)′/μ_(s)′⁰=10⁻⁵. Equations (11), (12),and (13) are important intermediate results, which provide generalizedexpressions for the analytical and numerical computation of themultiplicative weighting factors in the DCS Modified Beer-Lambert lawfor any homogeneous geometry.

One non-limiting assumption in this approach is that the correlationdiffusion equation accurately models the electric field auto-correlationfunction in tissue. This assumption is applicable to using largesource-detector separations, ρ□1/(μ_(a)+μ_(s)′), to measure highlyscattering media with isotropic dynamics. The DCS Modified Beer-Lambertlaw (Eq. (4)), however, can also be used for correlation transportconditions wherein the correlation diffusion equation breaks down. Inthis case, the derivatives in Eqs. (11) and (12) will have to be appliedto the solutions of the so-called correlation transport equation, whichcan be solved numerically with Monte Carlo techniques.

Appendix 2

The semi-infinite solution to the correlation diffusion equation (Eq.(5)) is approximately exponential in the small delay-time limit, i.e.,g₁(τ)≈exp(−γFτ), with γ≡K₀(μ_(s)′/μ_(a))k₀ ²r₁. Normalizing thedelay-time by the characteristic decay-time, i.e., τ_(c)=(γF)⁻¹ is ameaningful dimensionless way to express delay-times (FIGS. 12, 14),e.g., g₁≈0.4 for τγF=1. Further, the DCS Modified Beer-Lambert law (Eq.(4)) is a good approximation in the small delay-time limit because−log(g₂(τ)−1)=−log(βg₁ ²)=2γτF−log(β) is linear with respect to F.

To derive the small delay-time limit of the semi-infinite correlationdiffusion solution, first note that if the source-detector separation,ρ, is much greater than the photon transport mean-free path throughtissue, l_(tr), then

$\begin{matrix}{{r_{b} \approx {r_{1}( {1 + {x/r_{1}^{2}}} )}},{\frac{1}{r_{b}} \approx {\frac{1}{r_{1}}( {1 - \frac{x}{r_{1}^{2}}} )}},} & (14)\end{matrix}$

where x≡2z_(b)(z_(b)+l_(tr)). Substituting Eq. (14) into Eq. (2), we seethat

$\begin{matrix}{{G_{1}(\tau)} = {\frac{3}{4\pi \; l_{tr}}{{\frac{\exp ( {{- {K(\tau)}}r_{1}} )}{r_{1}}\lbrack {1 - {{\exp ( {{- {K(\tau)}}{x/r_{1}}} )}( {1 - \frac{x}{r_{1}^{2}}} )}} \rbrack}.}}} & (15)\end{matrix}$

In the limit K(τ)x/r₁□1, which is satisfied at small delay-times, Eq.(15) simplifies further to

$\begin{matrix}{{G_{1}(\tau)} \approx {\frac{x\; {\exp ( {{- {K(\tau)}}r_{1}} )}}{r_{1}^{2}}{( {{K(\tau)} + \frac{1}{r_{1}}} ).}}} & (16)\end{matrix}$

In the more stringent limit 2(μ_(s)′/μ_(a))k₀ ²Fτ□1, the electric fieldauto-correlation function in Eq. (16) is approximately exponential:

$\begin{matrix}{{{g_{1}(\tau)} = {\frac{G_{1}(\tau)}{G_{1}(0)} \approx {{\exp ( {{- \gamma}\; F\; \tau} )}( {1 + \frac{\gamma \; F\; \tau}{{r_{1}K_{0}} + 1}} )} \approx {\exp ( {{- \gamma}\; F\; \tau} )}}},} & (17)\end{matrix}$

where γ=K₀k₀ ²r₁(μ_(s)′/μ_(a)) and K₀≡K(0)=[3μ_(a)(μ_(a)+μ_(s)′)]^(1/2).

Appendix 3

All animal procedures were in accordance with applicable guidelines. OneDCS source-detector pair and one NIRS/DOS source-detector pair were usedfor hemodynamic monitoring. The positions of these fibers, denoted as(lateral distance from the center of the eye, lateral distance frommidline), are (10 mm, 15 mm), (21 mm, 5 mm), (26 mm, 5 mm), and (37 mm,15 mm) for the DCS source, DCS detector, NIRS/DOS source, and NIRS/DOSdetector, respectively. Thus, the source-detector separations for boththe NIRS/DOS and DCS pairs are approximately 15 mm.

Upon completion of the surgical preparation, the ventilation of the pigwas switched to a mixture of oxygen and nitrogen (3:7) with noisoflurane. Anesthesia was maintained instead with intravenousadministration of ketamine (60 mg/kg/h). Throughout the rest of thestudy, arterial oxygen saturation and end-tidal CO₂ were continuallymonitored with blood gas samples from the femoral artery and with acapnograph, respectively. The ventilation rate was initially adjusted tomaintain an end-tidal CO₂ between 40 and 50 mm Hg.

After inserting ninety-degree bend terminated optical fibers (FiberopticSystems, Simi Valley, Calif.) in the burr holes, a 5-pound sandbagweight was carefully placed on top of the fibers to secure them inplace. Two 1-mm diameter multi-mode borosilicate fibers (FiberopticSystems) delivered source light to the cerebral tissue, and a third 1-mmdiameter multi-mode fiber received diffusing light from the tissue forNIRS/DOS detection. For DCS detection, a 4×1 bundle of 780HP single-modefibers (Fiberoptic Systems) was used. These fibers interfaced to aportable custom-built instrument designed for hemodynamic monitoring. Inthe DCS measurement, a continuous wave, long coherence length 785 nmlaser (CrystaLaser Inc., Reno, Nev.) was employed to deliver sourcelight, and the outputs from an array of 4 high sensitivity avalanchephotodiodes (SPCM-AQ4C, Excelitas, Canada) operating in photon countingmode were connected to a multiple τ hardware correlator (Correlator.com,Bridgewater, N.J.). In the NIRS/DOS measurement, three lasers (690 nm785 nm, 830 nm; OZ Optics, Canada) intensity modulated at 70 MHz werecoupled to an optical switch, which sequentially cycled the source lightbetween the three wavelengths. A heterodyne detection scheme using aphotomultiplier tube (R928, Hamamatsu, Bridgewater, N.J.) was employedfor NIRS/DOS detection. The data acquisition was interleaved betweenNIRS/DOS and DCS.

After ten minutes of “baseline” cerebral hemodynamic monitoring in thepig, the drug dinitrophenol (DNP, 9 mg/kg) was injected intravenouslyover an hour to dramatically increase cerebral blood flow and oxygenmetabolism. The oxygen content in the ventilated gas was increased asneeded to maintain the arterial oxygen saturation in the pig above 95%.

Probe Pressure Modulation Algorithm for Oxygenation Monitoring withDOS/NIRS

An analogous probe pressure modulation scheme to DCS can be used tocalibrate continuous wave DOS/NIRS for monitoring of cerebraloxy-hemoglobin (HbO_(c)) and deoxy-hemoglobin (HbR_(c)) concentrations.This scheme employs a two-layer Modified Beer-Lambert framework whereintissue scattering is constant. It is often a reasonable approximation toassume that scattering effects on optical density changes are negligiblewhen compared against absorption effects.

Following analogous steps to those outliure ned for flow monitoring,DOS/NIRS measurements of light intensity are made at a longsource-detector separation, I(ρ_(l)), and a short source-detectorseparation, I(ρ_(s)). Using a two-layer model of the head, the DOS/NIRStwo-layer Modified Beer-Lambert laws are

$\begin{matrix}{{{\Delta \mspace{11mu} {OD}^{long}} \equiv {- {\log \lbrack \frac{I( \rho_{l} )}{I^{0}( \rho_{l} )} \rbrack}}} = {{{L_{c}( \rho_{l} )}{\Delta\mu}_{a,c}} + {{L_{ec}( \rho_{l} )}{\Delta\mu}_{a,{ec}}}}} & (1.1) \\{{{\Delta \; {OD}^{short}} \equiv {- {\log \lbrack \frac{I( \rho_{s} )}{I^{0}( \rho_{s} )} \rbrack}}} = {{L_{ec}( \rho_{s} )}{\Delta\mu}_{a,{ec}}}} & (1.2)\end{matrix}$

The cerebral and extra-cerebral tissue absorption and scatteringcoefficients that give rise to the measured intensities I(ρ_(l)) andI(ρ_(s)) are μ_(a,c), μ_(a,ec), μ_(s,c)′, and μ_(s,ec)′, respectively.Similarly, at the baseline measured intensities I⁰(ρ_(l)) and I⁰(ρ_(s)),the baseline cerebral and extra-cerebral tissue absorption andscattering coefficients are μ_(a,c) ⁰, μ_(a,ec) ⁰, μ_(s,c)′⁰ andμ_(s,ec)′⁰, respectively. The differential changes of cerebral andextra-cerebral absorption from baseline are Δμ_(a,c)≡μ_(a,c)−μ_(a,c) ⁰and Δμ_(a,ec)≡μ_(a,ec)−μ_(a,ec) ⁰. Finally, the partial pathlengthsL_(c)(ρ_(l))≡∂OD^(long,0)/∂μ_(a,c),L_(ec)(ρ_(l))≡∂OD^(long,0)/∂μ_(a,ec), andL_(ec)(ρ_(s))≡∂OD^(short,0)/∂μ_(a,ec) are the mean pathlengths that thedetected light travels through the cerebral (c) and extra-cerebral (ec)layers. It is assumed that detected light from the short separation doesnot sample the brain, and consequentially, L_(c)(ρ_(s))=0 andL_(ec)(ρ_(s)) is approximately the semi-infinite differentialpathlength.

Solving Eqs. (1.1) and (1.2) and for Δμ_(a,c), one may obtain

$\begin{matrix}{{\Delta\mu}_{a,c} = {{\frac{1}{L_{c}( \rho_{l} )}\lbrack {{\Delta \; {OD}^{long}} - {\frac{L_{ec}( \rho_{l} )}{L_{ec}( \rho_{s} )}\Delta \; {OD}^{short}}} \rbrack}.}} & (1.3)\end{matrix}$

The key advantage of using probe pressure modulation with DOS/NIRS isthat it enables direct measurement of the ratioL_(ec)(ρ_(l))/L_(ec)(ρ_(s)).

The ratio L_(ec)(ρ_(l))/L_(ec)(ρ_(s)) can be directly measured fromdifferential short and long separation optical density changes betweenperturbed and baseline states wherein only the extra-cerebral absorptionis different. Probe pressure modulation is a simple way to inducecontrolled extra-cerebral absorption changes without affecting cerebralabsorption. For relating a perturbed state at probe pressure P to thebaseline state at probe pressure P⁰, Eqs. (1.1) and (1.2) simplify to

$\begin{matrix}{{{{\Delta \; {OD}^{{long},P}} \equiv {- {\log \lbrack \frac{I^{P}( \rho_{l} )}{I^{0}( \rho_{l} )} \rbrack}}} = {{L_{ec}( \rho_{l} )}{\Delta\mu}_{a,{ec}}^{P}}},} & (1.4) \\{{{{\Delta \; {OD}^{{short},P}} \equiv {- {\log \lbrack \frac{I^{P}( \rho_{s} )}{I^{0}( \rho_{s} )} \rbrack}}} = {{L_{ec}( \rho_{s} )}{\Delta\mu}_{a,{ec}}^{P}}},} & (1.5)\end{matrix}$

where I^(P)(ρ_(l)) and I^(P) (ρ_(s)) are the measured intensities atprobe pressure P, and Δμ_(a,ec) ^(P)≡μ_(a,ec) ^(P)−μ_(a,ec) ⁰ is thepressure-induced extra-cerebral absorption change.

Dividing by and then substituting the result into (1.3), we obtain

$\begin{matrix}{{\Delta\mu}_{a,c} = {{\frac{1}{L_{c}( \rho_{l} )}\lbrack {{\Delta \; {OD}^{long}} - {\frac{\Delta \; {OD}^{{long},P}}{\Delta \; {OD}^{{short},P}}\Delta \; {OD}^{short}}} \rbrack}.}} & (1.6)\end{matrix}$

Here, intensity measurements at long and short separations along withinitial calibration measurements at two probe pressures determinesΔμ_(a,c) within a multiplicative proportionality constant,1/L_(c)(ρ_(l)). For accurately estimating the magnitude of the cerebralabsorption change, L_(c)(ρ_(l)) is calculated by numerically computingthe derivative of the continuous wave two-layer photon diffusion Green'sfunction, Φ(ρ_(l)), evaluated at the baseline tissue optical properties:

$\begin{matrix}{{{L_{c}( \rho_{l} )} = {{\frac{\partial}{\partial\mu_{a,c}}( {- {\log \lbrack {\Phi ( \rho_{l} )} \rbrack}} )} \approx {\frac{1}{{\Delta\mu}_{a,c}}{\log \lbrack \frac{\Phi ( {\rho_{l},{\mu_{a,c}^{0} - {{\Delta\mu}_{a,c}/2}},\mu_{a,{ec}}^{0},\mu_{s,c}^{\prime 0},\mu_{s,{ec}}^{\prime 0},l} )}{\Phi ( {\rho_{l},{\mu_{a,c}^{0} + {{\Delta\mu}_{a,c}/2}},\mu_{a,{ec}}^{0},\mu_{s,c}^{\prime 0},\mu_{s,{ec}}^{\prime 0},l} )} \rbrack}}}},} & (1.7)\end{matrix}$

where Δμ_(a,c)/μ_(a,c) ⁰=10⁻⁵. The Green's function Φ(ρ_(l)) can beevaluated using the analytical two-layer solution, or it can also beevaluated numerically using Monte Carlo techniques. The computation ofL_(c)(ρ_(l)) requires knowledge of μ_(a,c) ⁰, μ_(a,ec) ⁰, μ_(s,c)′⁰.μ_(s,ec)′⁰, and l. Ideally the extra-cerebral layer thickness is known apriori from anatomical information, and the tissue baseline opticalproperties are measured (e.g., with time-domain techniques). If a priorianatomical information and instrumentation for measuring baselineoptical properties is not available, then the baseline opticalproperties need to be assumed. The extra-cerebral layer thickness caneither also be assumed or estimated from the two-layer fit of DCS dataat multiple probe pressures from the DCS pressure algorithm.

Cerebral absorption determined from (1.6) will not be affected byextra-cerebral absorption changes to the extent that the two-layer modelaccurately models the head.

FIG. 31 is a flow chart summarizing the probe pressure modulationalgorithm for cerebral tissue absorption monitoring (Δμ_(a,c)) withDOS/NIRS. As shown in that figure, in the calibration stage, baselinelong and short separation intensities measured at probe pressureP⁰(I⁰(ρ_(l)), I⁰(ρ_(s))) and at probe pressure P≠P⁰(I^(P)(ρ_(l)),I^(P)(ρ_(s))) are used to calculate ΔOD^(long,P) and ΔOD^(short,P),which are then used to estimate L_(ec)(ρ_(l))/L_(ec)(ρ_(s)) (“DOSCalibration term 1). “DOS Calibration term 2” is the numericalevaluation of L_(c)(ρ_(l)), which requires knowledge of the baselinetissue optical properties and the extra-cerebral layer thickness (l).Ideally, these baseline tissue properties are measured. In themonitoring stage, DOS Calibration terms 1 and 2 are employed to convertsubsequent measurements of differential long and short separationoptical density changes, i.e., ΔOD^(long) and ΔOD^(short), todifferential cerebral absorption changes. Note that the baseline usedfor the calibration stage and for the monitoring stage is the same.

The cerebral tissue absorption coefficient depends linearly on theconcentrations of tissue chromophores. With NIR light, changes incerebral absorption predominantly arise from changes in cerebraloxygenated hemoglobin (HbO_(e)) and de-oxygenated hemoglobin (HbR_(c))concentrations, such that

Δμ_(a,c)(ρ_(l),λ)≈ε_(HbO)(λ)ΔHbO _(c)+ε_(HbR)(λ)ΔHbR _(c).  (1.8)

Here, ε_(HbO)(λ) and ε_(HbR)(λ) are wavelength-dependent extinctioncoefficients for oxygenated hemoglobin and de-oxygenated hemoglobin,which are both known and tabulated as a function of wavelength λ, andΔHbO_(c) and ΔHbR_(c) are differential changes in cerebral oxygenatedand de-oxygenated hemoglobin concentration from baseline. Formultispectral cerebral absorption monitoring with (1.6) and (1.8)becomes a system of equations, i.e., one equation for each wavelength,which can then be solved for ΔHbO_(c) and ΔHbR_(c). In some embodiments,two wavelengths are used to solve for these two chromophores.

Finally, the baseline cerebral hemoglobin concentrations HbO_(c) ⁰ andHbR_(c) ⁰ can be calculated from multispectral measurements of μ_(a,c)⁰(λ), which in turn enables the computation of cerebral tissue oxygensaturation, StO_(2,c):

${StO}_{2,c} = {\frac{{HbO}_{c}^{0} + {\Delta \; {HbO}_{c}}}{{HbO}_{c}^{0} + \; {HbR}_{c}^{0} + {\Delta \; {HbO}_{c}} + {\Delta \; {HbR}_{c}}}.}$

Combining DOS/NIRS measurements of StO_(2,c) with DCS measurements ofcerebral blood flow (F_(c)) permits monitoring of cerebral oxygenmetabolism. Any of the systems and/or components described herein may beconfigured to apply any aspect of the foregoing DCS, DOS, and NIRSanalysis, e.g., the foregoing analysis of StO₂ and F_(c).

Additional Aspects and Embodiments

In one aspect, the present disclosure provides methods. The methodssuitably include measuring moving particles in a tissue. Such particlesinclude red blood cells, white blood cells, leukocytes, lymphocytes,muscle fibers, and the like. Additionally, the methods are suitable formeasuring exogenous moving particles, such as scattering contrast agents(e.g., ultrasound ‘microbubbles’). The disclosed methods are applicableto motion of any particle of living tissue; red blood cells areconsidered especially suitable.

Measuring suitably includes illuminating a first tissue region throughillumination of a second tissue region that is superficial to the firsttissue region. The first tissue region may be a blood vessel, a muscle,a bone, and the like. Cerebral tissue is a particularly suitable firsttissue region. As one example, a first tissue region may be cerebraltissue, and a second tissue region may be extracerebral tissue, e.g.,scalp, skull, cerebro-spinal fluid located proximate to the cerebraltissue.

Illumination may be effected with a first source-detector pair and witha second source-detector pair. The sources suitably provide theillumination, and the detectors collect illumination scattered by theparticles. Suitable illumination sources are long-coherence lengthlasers for DCS, and multi-mode lasers, LEDs, arc lamps, halogen lampsfor DOS, lasers and LEDs being most suitable. Suitable detectors includephoton counters, imagers, photodiodes, photo-multiplier tubes and thelike; photon counting avalanches photo diodes (APDs) are consideredparticularly suitable for DCS. Source-detector pairs may be maintainedin position by being secured by elastic, a Velcro™ band, a balloon, astrap, a garment, or by other securing means known to those of ordinaryskill in the art. The distance between sources and detectors may befixed, but may also be variable. In some embodiments, the user maychange the distance between the sources and detectors. It should beunderstood that in some embodiments, a single detector may collectillumination from one, two, or more sources. Two or more of such sourcesmay be separated from their common detector by different distances.Similarly, a single source can supply illumination (concurrently) to oneor more detectors, with different distances separating the common sourcefrom each detector.

The source and detector of the first source-detector pair are suitablyseparated by a first distance. Such a distance may be in the range offrom 0.1 mm to about 1 mm, or from about 1 mm to about 10 cm, or fromabout 10 mm to about 0.5 cm. The source and detector of the secondsource-detector pair are also suitably separated by a distance. Theseparation of the source and detector of the second pair is suitablygreater than the separation distance between the source and detector ofthe first pair. The separation of the source and detector of the secondpair is may be 1.0001 times, 1.1 times, 1.5 times, 2 times, 5 times, 10times, 100 times, 1000 times, or even 10,000 times the separationdistance between the source and detector of the first pair.

Collection of the illumination is suitably performed under applicationof (a) one or more perturbations directed to the second tissue region(superficial region), (b) one or more perturbations proximate to thelocation of the first source-detector pair, proximate to the secondsource source-detector pair, or proximate to both the first and secondsource-detector pairs, or (c) any combination of (a) and (b). It shouldbe understood that exposure to ambient conditions is considered aperturbation for purposes of this disclosure.

As an example, a user might collect illumination from the first andsecond detectors while the tissue is subjected to ambient pressure andthen collect illumination from the first and second detectors while thetissue is subjected to a pressure that is 10 mm Hg greater than ambientpressure. Exemplary, non-limiting perturbations include pressurevariation (positive and negative), thermal energy transfer (e.g.,application or removal of heat), illumination, fluid, electric field,electric current, chemical treatment, sonication, magnetic stimulation,and the like. In some embodiments, illumination is collected under twoor more conditions, two or more of which conditions differ in someaspect from ambient conditions. In other embodiments, illumination iscollected under ambient conditions and under one other condition thatdiffers in some aspect (e.g., pressure, temperature, humidity) fromambient conditions. The form of the perturbations can encompass a stepchange (e.g. ambient pressure to 10 mmHg greater than ambient pressure,and back to ambient pressure), or a modulation (e.g. pressure varyingsinusoidally between ambient and 10 mmHg greater than ambient) ofconditions.

A perturbation may be applied, in some embodiments, so as to effect ahemodynamic change in the second tissue region. Such a change may be achange in, e.g., blood flow, blood volume, or saturation. As oneexample, pressure may be applied to a subject's extracerebral region soas to reduce extracerebral blood flow in and/or around the location ofthe applied pressure.

Users may estimate a blood flow of the first tissue region from thecollected illumination. In one embodiment, this estimation may includeapplication of the DCS Modified Beer-Lambert law, application of theDOS/NIRS Modified Beer-Lambert Law, or any combination thereof, or anycombination thereof, all of which are described elsewhere herein. Insome embodiments, estimating blood flow may comprise application of theDCS Modified Beer-Lambert law for a multi-layer medium, e.g., atwo-layer medium, a three-layer medium, or other multi-layer medium. Asdescribed elsewhere herein, application of the DCS Modified Beer-Lambertlaw for a two-layer medium is considered particularly suitable for someapplications, including estimation of cerebral blood flow. In thatparticular application, extracerebral tissue is modeled as one layer,and cerebral tissue is modeled as another layer in the two-layer model.

In some embodiments, at least one of the parameters of the DCS ModifiedBeer-Lambert law is derived from illumination collected from a subject.In this way, the user may develop a model that is customized to aparticular subject. In some embodiments, at least one of the parametersof the DCS Modified Beer-Lambert law is derived from populationmeasurements. A population measurement may be a value based on two ormore subjects, e.g., an average value based on a measurement of sevensubjects. One may apply in the model one or more parameters derived fromthe subject under observation as well as one or more parameters derivedfrom population measurements.

Deriving a parameter may include, e.g., calculating a value related toillumination gathered when tissue is subject to ambient conditions orsubject to a perturbation such as pressure, a cold bar, and the like.The illumination may—as described elsewhere herein—be gathered from thefirst source-detector pair, from the second detector pair, or both.Deriving may comprise calculating a value related to illuminationgathered at (a) each of two pressures, (b) illumination gathered fromthe first source-detector pair, (c) illumination gathered from thesecond source-detector pair, or any combination of (a), (b), or (c).

One or more steps of the disclosed methods (including the estimation ofblood flow) may be based on illumination collected at a number of delaytime values, e.g., 1, 2, 3, 4, 5, or more delay time values. In someembodiments, the number of delay time values used is optimized to be theminimum number of delay time values to provide a sufficient or desiredsignal-to-noise ratio and sufficient measurement speed. In someembodiments, the one or more steps are based on illumination collectedat one delay time value. In some embodiments, there are 1-5 delay times,ranging between, e.g., 0.1 and 1000 microseconds.

A user may estimate the first tissue region hemodynamic quantity (e.g.,blood flow) from the collected illumination before, during, and/or afterdelivery of an agent to the subject. An agent may be a contrast agent, atreatment agent, an agonist, and the like. Contrast agents could includeindocyanine green (ICG, Cardio-Green, Akron Inc.), microbubbles utilizedfor ultrasound contrast, or boli/infusions of red blood cells,indocyanine green (ICG) for estimating absolute blood flow; alsomicrobubbles. A user may estimate the first tissue region blood flowbefore, during, and/or after the subject engages in an activity, e.g.,exercise, sleep, eating, treatment, and the like. A user may alsoestimate the blood flow during a procedure, e.g., surgery, stimulation,or other treatment. This estimation may be done in real time. Theestimation may also be done after the treatment. As described elsewhereherein, the disclosed methods may utilize DCS, DOS/NIRS, or anycombination thereof.

A user may also estimate the first tissue region blood flow before,during, and/or after physically manipulating the subject, or before,during and/or after any combination of the foregoing. As describedelsewhere herein, the user may estimate the first tissue region bloodflow from the collected illumination collected at a number of delay timevalues, including at a number optimized to be the minimum number ofdelay time values to provide a sufficient signal-to-noise ratio. A usermay also perform the estimation based on illumination collected at onedelay time value.

The present disclosure also provides systems. In one embodiment, asystem comprises a first illumination source-detector pair having asource and detector separated by a first distance (a); a secondillumination source-detector pair having a source and detector separatedby a second distance (b), distances (a) and (b) being different from oneanother; an element configured to apply a pressure between the systemand the subject's body; and a processor configured to estimate atissue's hemodynamic quantity (e.g., blood flow, blood volume, orsaturation) from illumination collected by at least one of thesource-detector pairs.

Suitable sources, detectors, source-detector pairs, and source-detectorseparations are described elsewhere herein. Balloons, pumps, servos,elastic bands, and other devices known to those of skill in the art areall suitable elements for applying a pressure between the system and thesubject's body. It should be understood, however, that the disclosedsystems may also include one or more elements configured to apply aperturbation other than pressure to the subject. As one example, asystem may include a heater, a cooler, an injector, a source of vacuum,and like elements configured to deliver one or more perturbations to thesubject. An element may be configured to apply a perturbation (e.g.,pressure, heat) proximate to at least one of the first and secondsource-detector pairs. As described elsewhere herein, a system mayinclude an accelerometer, which may be used to measure and account forthe effect of a subject's motion or an instrument's motion.

The disclosed systems may further comprise a device configured tocompute intensity correlation functions from photon counts. Such adevice may be in electronic communication, optical communication, orboth with at least one of the detectors of the first and secondsource-detector pairs. Suitable such devices include computers(stationary and portable), smartphones, tablet computers,microcontrollers and processors, field programmable gate arrays,electronic circuits and the like.

The systems may include one or more elements—e.g., a computer, a tablet,or even a processor—configured to isolate blood flow signals fromcollected illumination. The processor may be configured to carry out oneor more steps of the DCS Modified Beer-Lambert law, for example.

A system may include one or more detectors that are single-mode fibersor few-mode fibers. As described elsewhere herein, a detector of thesystem may be a photon-counting detector. In some embodiments, at leastone source and one detector share a prism. In some embodiments at leasttwo sources share a prism.

A user may use the described systems to measure a motion of movingparticles in a subject's tissue. One such motion is cerebral blood flow.

The present disclosure also provides additional methods of estimating ahemodynamic quantity (e.g., a cerebral blood flow, blood volume, orsaturation). These methods may include formulating a first estimate ofan extracerebral hemodynamic quantity, e.g., blood flow. This estimatemay include DCS measurement, DOS measurement, or both, as describedelsewhere herein.

The methods also include perturbing extracerebral tissue. Suitableperturbations—e.g., pressure application—are described elsewhere herein.A user may apply one, two, or more perturbations during the course of ahemodynamic quantity (e.g., blood flow) estimation.

A user may also formulate a second estimate of an extracerebralhemodynamic quantity (e.g, blood flow, blood volume). The secondestimate may be related to perturbation of extracerebral tissue, asdescribed elsewhere herein.

The methods also include formulating a final estimate of a cerebralhemodynamic quantity (e.g, blood flow) related at least in part (e.g.,an average, a weighted average) to the first and second estimates of theextracerebral hemodynamic quantity. The first estimate of theextracerebral hemodynamic quantity (e.g, blood flow) may be obtainedunder ambient conditions, but may also be related to perturbation ofextracerebral tissue. Thus, both estimates of extracerebral blood flowmay be related to perturbations of the extracerebral tissue.

The methods may also include formulating at least a first estimate ofthe cerebral hemodynamic quantity (e.g., blood flow). This estimate maybe based on DCS results. A user may also relate the final cerebralhemodynamic quantity estimate at least in part to an estimate of theextracerebral hemodynamic quantity and to the first estimate of thecerebral hemodynamic quantity.

In a further aspect, the present disclosure provides methods ofmonitoring a blood flow. (As described elsewhere herein, “blood flow” isillustrative only, and may be substituted for by blood volume,saturation, or other hemodynamic quantities.) These methods includeilluminating a tissue and a region superficial to the tissue. Suitableillumination techniques and illuminators are set forth elsewhere herein.A user may also apply and/or modulate one or more perturbations (e.g.,pressures, temperature changes, lighting changes, or even administeringone or more agents) to the region superficial to the tissue. A user mayalso collect a blood flow signal that is related to illuminationreflected by the tissue and to illumination reflected by the regionsuperficial to the tissue. A user may also remove from that signal atleast a portion of the illumination reflected by the region superficialto the tissue. This may also be characterized as removing from thatsignal the contribution to that signal from the illumination reflectedby the region superficial to the tissue.

In a further aspect, the present disclosure provides methods. Themethods suitably comprise measuring moving particles in a tissue, themeasuring comprising illuminating a first tissue region and illuminatinga second tissue region superficial to the first tissue region; with afirst source-detector pair and with a second source-detector pair,collecting illumination scattered by the particles, the source anddetector of the first source-detector pair being separated by a firstdistance, the source and detector of the second source-detector pairbeing separated by a second distance, the second distance being greaterthan the first distance, the collecting being performed underapplication of (a) one or more perturbations directed to the secondtissue region, (b) one or more perturbations proximate to the locationof the first source-detector pair, proximate to the second sourcesource-detector pair, or proximate to both the first and secondsource-detector pairs, or (c) any combination of (a) and (b), at leastone perturbation effecting a hemodynamic change in the second tissueregion, and estimating a hemodynamic quantity (e.g., blood flow) of thefirst tissue region from the collected illumination, wherein theestimating comprises application of the DOS/NIRS Modified Beer-Lambertlaw.

It should also be understood that systems according to any of thepreceding aspects may be configure to collect DCS information, DOS/NIRSinformation, or both. A system may include a processor that isconfigured to collect and/or process either type of information. Asystem may be dedicated to DCS or DOS/NIRS, or may be switchable betweenthe two.

1. A method, comprising: measuring moving particles in a tissue, themeasuring comprising illuminating a first tissue region and illuminatinga second tissue region superficial to the first tissue region; with afirst source-detector pair and with a second source-detector pair,collecting illumination scattered by the particles, the source anddetector of the first source-detector pair being separated by a firstdistance, the source and detector of the second source-detector pairbeing separated by a second distance, the second distance being greaterthan the first distance, the collecting being performed underapplication of (a) one or more perturbations directed to the secondtissue region, (b) one or more perturbations proximate to the locationof the first source-detector pair, proximate to the second sourcesource-detector pair, or proximate to both the first and secondsource-detector pairs, or (c) any combination of (a) and (b), at leastone perturbation effecting a hemodynamic change in the second tissueregion, and estimating a hemodynamic quantity of the first tissue regionfrom the collected illumination.
 2. The method of claim 1, wherein theestimating comprises application of the DCS Modified Beer-Lambert law,application of the DOS/NIRS Modified Beer-Lambert Law, or anycombination thereof.
 3. The method of claim 2, wherein the estimatingcomprises application of the DCS Modified Beer-Lambert law, applicationof the DOS/NIRS Modified Beer-Lambert Law, or any combination thereof,for a multi-layer medium.
 4. The method of claim 3, wherein theestimating comprises application of the DCS Modified Beer-Lambert law,application of the DOS/NIRS Modified Beer-Lambert Law, or anycombination thereof, for a two-layer medium.
 5. The method of claim 2,wherein at least one of the parameters of the DCS Modified Beer-Lambertlaw, application of the DOS/NIRS Modified Beer-Lambert Law, or anycombination thereof, is derived from illumination collected from thesubject.
 6. The method of claim 2, wherein at least one of theparameters of the DCS Modified Beer-Lambert law, application of theDOS/NIRS Modified Beer-Lambert Law, or any combination thereof, isderived from population measurements.
 7. The method of claim 5, whereinthe deriving comprises calculating a value related to illuminationgathered at (a) each of two pressures, (b) illumination gathered fromthe first source-detector pair, (c) illumination gathered from thesecond source-detector pair, or any combination of (a), (b), or (c). 8.The method of claim 1, wherein the estimating is based on illuminationcollected at a number of delay time values optimized to be the minimumnumber of delay time values to provide a sufficient signal-to-noiseratio.
 9. The method of claim 1, wherein the estimating is based onillumination collected at one delay time value.
 10. The method of claim1, further comprising estimating the first tissue hemodynamic quantityfrom the collected illumination (a) before, during, and/or afterdelivery of an agent to the subject, (b) before, during, and/or afterthe subject engages in an activity, (c) before, during, and/or afterphysically manipulating the subject, or any combination of theforegoing.
 11. The method of claim 1, wherein estimating the firsttissue region hemodynamic quantity from the collected illuminationanalyzed at the number of delay time values optimized to be the minimumnumber of delay time values to provide a sufficient signal-to-noiseratio.
 12. The method of any claim 1, wherein the estimating is based onillumination collected at one delay time value.
 13. The method of claim1, further comprising measuring a motion of moving particles in asubject's tissue.
 14. The method of claim 13, wherein the motioncomprises a cerebral blood flow.
 15. A method of estimating ahemodynamic quantity, comprising: formulating a first estimate of anextracerebral hemodynamic quantity; perturbing extracerebral tissue;formulating a second estimate of an extracerebral hemodynamic quantityrelated to the perturbation of extracerebral tissue; and formulating afinal estimate of the hemodynamic quantity related at least in part tothe first and second estimates of extracerebral blood flow.
 16. Themethod of claim 15, wherein the first estimate of the extracerebralhemodynamic quantity is related to a perturbation of extracerebraltissue.
 17. The method of claim 15, further comprising formulating atleast a first estimate of a cerebral hemodynamic quantity.
 18. Themethod of claim 17, further comprising relating the final cerebralhemodynamic quantity estimate at least in part to an estimate of anextracerebral hemodynamic quantity and to the first estimate of thecerebral hemodynamic quantity.
 19. A method of monitoring a blood flow,comprising: illuminating a tissue and a region superficial to thetissue; modulating one or more pressures applied to the regionsuperficial to the tissue; collecting a blood flow signal related toillumination reflected by the tissue and to illumination reflected bythe region superficial to the tissue; and removing from the signal atleast a portion of the illumination reflected by the region superficialto the tissue.
 20. A method, comprising: measuring moving particles in atissue, the measuring comprising illuminating a first tissue region andilluminating a second tissue region superficial to the first tissueregion; with a first source-detector pair and with a secondsource-detector pair, collecting illumination scattered by theparticles, the source and detector of the first source-detector pairbeing separated by a first distance, the source and detector of thesecond source-detector pair being separated by a second distance, thesecond distance being greater than the first distance, the collectingbeing performed under application of (a) one or more perturbationsdirected to the second tissue region, (b) one or more perturbationsproximate to the location of the first source-detector pair, proximateto the second source source-detector pair, or proximate to both thefirst and second source-detector pairs, or (c) any combination of (a)and (b), at least one perturbation effecting a hemodynamic change in thesecond tissue region, and estimating a blood flow of the first tissueregion from the collected illumination, wherein the estimating comprisesapplication of the DOS/NIRS Modified Beer-Lambert law.